%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI687_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep  6 17:02:36 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Proof 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ARI687_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Aug 30 02:01:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  % SZS output start Proof
% 0.19/0.51  tff(y_type, type, (
% 0.19/0.51     y: $int)).
% 0.19/0.51  tff(x_type, type, (
% 0.19/0.51     x: $int)).
% 0.19/0.51  tff(1,plain,
% 0.19/0.51      ((0 = $sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y)))))) <=> ($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))) = 0)),
% 0.19/0.51      inference(commutativity,[status(thm)],[])).
% 0.19/0.51  tff(2,plain,
% 0.19/0.51      (($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))) = 0) <=> (0 = $sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))))),
% 0.19/0.51      inference(symmetry,[status(thm)],[1])).
% 0.19/0.51  tff(3,plain,
% 0.19/0.51      (($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0) <=> ($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))) = 0)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(4,plain,
% 0.19/0.51      (($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0) <=> ($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(5,plain,
% 0.19/0.51      (($sum($sum($sum($product($product($product(x, x), x), y), $product($product(x, x), y)), $product($product($product(3, x), x), x)), $product($product(2, x), x)) = 0) <=> ($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(6,axiom,($sum($sum($sum($product($product($product(x, x), x), y), $product($product(x, x), y)), $product($product($product(3, x), x), x)), $product($product(2, x), x)) = 0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq1')).
% 0.19/0.51  tff(7,plain,
% 0.19/0.51      ($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0),
% 0.19/0.51      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.51  tff(8,plain,
% 0.19/0.51      ($sum($product(x, $product(x, $product(x, y))), $sum($product(x, $product(x, y)), $sum($product(3, $product(x, $product(x, x))), $product(2, $product(x, x))))) = 0),
% 0.19/0.51      inference(modus_ponens,[status(thm)],[7, 4])).
% 0.19/0.51  tff(9,plain,
% 0.19/0.51      ($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))) = 0),
% 0.19/0.51      inference(modus_ponens,[status(thm)],[8, 3])).
% 0.19/0.51  tff(10,plain,
% 0.19/0.51      (0 = $sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y)))))),
% 0.19/0.51      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.51  tff(11,plain,
% 0.19/0.51      ((~(0 = $sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))))) | $greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)),
% 0.19/0.51      inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51  tff(12,plain,
% 0.19/0.51      ($greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)),
% 0.19/0.51      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.51  tff(13,assumption,(~$greatereq($product(x, x), 0)), introduced(assumption)).
% 0.19/0.51  tff(14,plain,
% 0.19/0.51      ($greatereq($product(x, x), 0)),
% 0.19/0.51      inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51  tff(15,plain,
% 0.19/0.51      ($false),
% 0.19/0.51      inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.51  tff(16,plain,($greatereq($product(x, x), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51  tff(17,assumption,(~$greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)), introduced(assumption)).
% 0.19/0.51  tff(18,assumption,(~$greatereq(x, 0)), introduced(assumption)).
% 0.19/0.51  tff(19,plain,
% 0.19/0.51      ($greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | $greatereq(x, 0)),
% 0.19/0.51      inference(theory_lemma,[status(thm)],[])).
% 0.19/0.51  tff(20,plain,
% 0.19/0.51      ($false),
% 0.19/0.51      inference(unit_resolution,[status(thm)],[19, 17, 18])).
% 0.19/0.51  tff(21,plain,($greatereq(x, 0) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51  tff(22,plain,
% 0.19/0.51      ($greatereq(x, 0)),
% 0.19/0.51      inference(unit_resolution,[status(thm)],[21, 17])).
% 0.19/0.51  tff(23,plain,
% 0.19/0.51      ((3 = $sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y)))))))))) <=> ($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))) = 3)),
% 0.19/0.51      inference(commutativity,[status(thm)],[])).
% 0.19/0.51  tff(24,plain,
% 0.19/0.51      (($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))) = 3) <=> (3 = $sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))))),
% 0.19/0.51      inference(symmetry,[status(thm)],[23])).
% 0.19/0.51  tff(25,plain,
% 0.19/0.51      (($sum($product(-3, x), $sum($product(-2, $product(x, x)), $sum($product(-1, y), $sum($product(-1, $product(x, y)), $sum($product(6, $product(x, $product(x, x))), $product(2, $product(x, $product(x, $product(x, y))))))))) = -3) <=> ($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))) = 3)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(26,plain,
% 0.19/0.51      ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = $sum($product(-3, x), $sum($product(-2, $product(x, x)), $sum($product(-1, y), $sum($product(-1, $product(x, y)), $sum($product(6, $product(x, $product(x, x))), $product(2, $product(x, $product(x, $product(x, y)))))))))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(27,plain,
% 0.19/0.51      (($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3) <=> ($sum($product(-3, x), $sum($product(-2, $product(x, x)), $sum($product(-1, y), $sum($product(-1, $product(x, y)), $sum($product(6, $product(x, $product(x, x))), $product(2, $product(x, $product(x, $product(x, y))))))))) = -3)),
% 0.19/0.51      inference(monotonicity,[status(thm)],[26])).
% 0.19/0.51  tff(28,plain,
% 0.19/0.51      (($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3) <=> ($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))) = 3)),
% 0.19/0.51      inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.51  tff(29,plain,
% 0.19/0.51      (($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3) <=> ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(30,plain,
% 0.19/0.51      (($sum(3, $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x))))))) = 0) <=> ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(31,plain,
% 0.19/0.51      ($sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))), 3) = $sum(3, $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(32,plain,
% 0.19/0.51      ($sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $product(-2, $product(x, x)))))), $product(-3, x)) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x))))))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(33,plain,
% 0.19/0.51      ($product(-1, $product(3, x)) = $product(-3, x)),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(34,plain,
% 0.19/0.51      ($sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $product(6, $product(x, $product(x, x)))))), $product(-2, $product(x, x))) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $product(-2, $product(x, x))))))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(35,plain,
% 0.19/0.51      ($product(-1, $product(2, $product(x, x))) = $product(-2, $product(x, x))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(36,plain,
% 0.19/0.51      ($product($product(2, x), x) = $product(2, $product(x, x))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(37,plain,
% 0.19/0.51      ($product(-1, $product($product(2, x), x)) = $product(-1, $product(2, $product(x, x)))),
% 0.19/0.51      inference(monotonicity,[status(thm)],[36])).
% 0.19/0.51  tff(38,plain,
% 0.19/0.51      ($product(-1, $product($product(2, x), x)) = $product(-2, $product(x, x))),
% 0.19/0.51      inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.51  tff(39,plain,
% 0.19/0.51      ($sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $product(-1, y))), $product(6, $product(x, $product(x, x)))) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $product(6, $product(x, $product(x, x))))))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(40,plain,
% 0.19/0.51      ($product($product(6, $product(x, x)), x) = $product(6, $product(x, $product(x, x)))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(41,plain,
% 0.19/0.51      ($product($product(6, x), x) = $product(6, $product(x, x))),
% 0.19/0.51      inference(rewrite,[status(thm)],[])).
% 0.19/0.51  tff(42,plain,
% 0.19/0.51      ($product($product($product(6, x), x), x) = $product($product(6, $product(x, x)), x)),
% 0.19/0.51      inference(monotonicity,[status(thm)],[41])).
% 0.19/0.51  tff(43,plain,
% 0.19/0.51      ($product($product($product(6, x), x), x) = $product(6, $product(x, $product(x, x)))),
% 0.19/0.51      inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.51  tff(44,plain,
% 0.19/0.51      ($sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y))), $product(-1, y)) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $product(-1, y)))),
% 0.19/0.52      inference(rewrite,[status(thm)],[])).
% 0.19/0.52  tff(45,plain,
% 0.19/0.52      ($difference($sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y))), y) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y))), $product(-1, y))),
% 0.19/0.52      inference(rewrite,[status(thm)],[])).
% 0.19/0.52  tff(46,plain,
% 0.19/0.52      ($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y)))),
% 0.19/0.52      inference(rewrite,[status(thm)],[])).
% 0.19/0.52  tff(47,plain,
% 0.19/0.52      ($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y) = $difference($sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y))), y)),
% 0.19/0.52      inference(monotonicity,[status(thm)],[46])).
% 0.19/0.52  tff(48,plain,
% 0.19/0.52      ($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $product(-1, $product(x, y))), $product(-1, y))),
% 0.19/0.52      inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.52  tff(49,plain,
% 0.19/0.52      ($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $product(-1, y)))),
% 0.19/0.52      inference(transitivity,[status(thm)],[48, 44])).
% 0.19/0.52  tff(50,plain,
% 0.19/0.52      ($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $product(-1, y))), $product(6, $product(x, $product(x, x))))),
% 0.19/0.52      inference(monotonicity,[status(thm)],[49, 43])).
% 0.19/0.52  tff(51,plain,
% 0.19/0.52      ($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $product(6, $product(x, $product(x, x))))))),
% 0.19/0.52      inference(transitivity,[status(thm)],[50, 39])).
% 0.19/0.52  tff(52,plain,
% 0.19/0.52      ($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $product(6, $product(x, $product(x, x)))))), $product(-2, $product(x, x)))),
% 0.19/0.52      inference(monotonicity,[status(thm)],[51, 38])).
% 0.19/0.52  tff(53,plain,
% 0.19/0.52      ($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $product(-2, $product(x, x))))))),
% 0.19/0.52      inference(transitivity,[status(thm)],[52, 34])).
% 0.19/0.52  tff(54,plain,
% 0.19/0.52      ($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $product(-2, $product(x, x)))))), $product(-3, x))),
% 0.19/0.52      inference(monotonicity,[status(thm)],[53, 33])).
% 0.19/0.52  tff(55,plain,
% 0.19/0.52      ($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))) = $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x))))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[54, 32])).
% 0.52/0.52  tff(56,plain,
% 0.52/0.52      ($sum($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))), 3) = $sum($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))), 3)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[55])).
% 0.52/0.52  tff(57,plain,
% 0.52/0.52      ($sum($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))), 3) = $sum(3, $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[56, 31])).
% 0.52/0.52  tff(58,plain,
% 0.52/0.52      (($sum($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))), 3) = 0) <=> ($sum(3, $sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x))))))) = 0)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[57])).
% 0.52/0.52  tff(59,plain,
% 0.52/0.52      (($sum($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))), 3) = 0) <=> ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3)),
% 0.52/0.52      inference(transitivity,[status(thm)],[58, 30])).
% 0.52/0.52  tff(60,axiom,($sum($sum($sum($sum($difference($sum($product($product($product($product(2, x), x), x), y), $product(-1, $product(x, y))), y), $product($product($product(6, x), x), x)), $product(-1, $product($product(2, x), x))), $product(-1, $product(3, x))), 3) = 0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq2')).
% 0.52/0.52  tff(61,plain,
% 0.52/0.52      ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[60, 59])).
% 0.52/0.52  tff(62,plain,
% 0.52/0.52      ($sum($product(2, $product(x, $product(x, $product(x, y)))), $sum($product(-1, $product(x, y)), $sum($product(-1, y), $sum($product(6, $product(x, $product(x, x))), $sum($product(-2, $product(x, x)), $product(-3, x)))))) = -3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[61, 29])).
% 0.52/0.52  tff(63,plain,
% 0.52/0.52      ($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))) = 3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[62, 28])).
% 0.52/0.52  tff(64,plain,
% 0.52/0.52      (3 = $sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y)))))))))),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[63, 24])).
% 0.52/0.52  tff(65,plain,
% 0.52/0.52      ((~(3 = $sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))))) | $greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)),
% 0.52/0.52      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.52  tff(66,plain,
% 0.52/0.52      ($greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)),
% 0.52/0.52      inference(unit_resolution,[status(thm)],[65, 64])).
% 0.52/0.52  tff(67,plain,
% 0.52/0.52      ((3 = $sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y)))))))) <=> ($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))) = 3)),
% 0.52/0.52      inference(commutativity,[status(thm)],[])).
% 0.52/0.52  tff(68,plain,
% 0.52/0.52      (($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))) = 3) <=> (3 = $sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))))),
% 0.52/0.52      inference(symmetry,[status(thm)],[67])).
% 0.52/0.52  tff(69,plain,
% 0.52/0.52      (($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3) <=> ($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))) = 3)),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(70,plain,
% 0.52/0.52      (($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3) <=> ($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3)),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(71,plain,
% 0.52/0.52      (($sum(-3, $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x)))))) = 0) <=> ($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3)),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(72,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), -3) = $sum(-3, $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(73,plain,
% 0.52/0.52      ($product(-1, 3) = -3),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(74,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), $product(-1, 3)) = $sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), -3)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[73])).
% 0.52/0.52  tff(75,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), $product(-1, 3)) = $sum(-3, $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[74, 72])).
% 0.52/0.52  tff(76,plain,
% 0.52/0.52      ($difference($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), 3) = $sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), $product(-1, 3))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(77,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $product(9, $product(x, x))))), $product(5, x)) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x)))))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(78,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), y)), $product(9, $product(x, x))) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $product(9, $product(x, x)))))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(79,plain,
% 0.52/0.52      ($product($product(9, x), x) = $product(9, $product(x, x))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(80,plain,
% 0.52/0.52      ($sum($sum($product(3, $product(x, $product(x, y))), $product(2, $product(x, y))), y) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), y))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(81,plain,
% 0.52/0.52      ($sum($product($product($product(3, x), x), y), $product($product(2, x), y)) = $sum($product(3, $product(x, $product(x, y))), $product(2, $product(x, y)))),
% 0.52/0.52      inference(rewrite,[status(thm)],[])).
% 0.52/0.52  tff(82,plain,
% 0.52/0.52      ($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y) = $sum($sum($product(3, $product(x, $product(x, y))), $product(2, $product(x, y))), y)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[81])).
% 0.52/0.52  tff(83,plain,
% 0.52/0.52      ($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), y))),
% 0.52/0.52      inference(transitivity,[status(thm)],[82, 80])).
% 0.52/0.52  tff(84,plain,
% 0.52/0.52      ($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)) = $sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), y)), $product(9, $product(x, x)))),
% 0.52/0.52      inference(monotonicity,[status(thm)],[83, 79])).
% 0.52/0.52  tff(85,plain,
% 0.52/0.52      ($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $product(9, $product(x, x)))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[84, 78])).
% 0.52/0.52  tff(86,plain,
% 0.52/0.52      ($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)) = $sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $product(9, $product(x, x))))), $product(5, x))),
% 0.52/0.52      inference(monotonicity,[status(thm)],[85])).
% 0.52/0.52  tff(87,plain,
% 0.52/0.52      ($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)) = $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x)))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[86, 77])).
% 0.52/0.52  tff(88,plain,
% 0.52/0.52      ($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = $difference($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), 3)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[87])).
% 0.52/0.52  tff(89,plain,
% 0.52/0.52      ($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = $sum($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))), $product(-1, 3))),
% 0.52/0.52      inference(transitivity,[status(thm)],[88, 76])).
% 0.52/0.52  tff(90,plain,
% 0.52/0.52      ($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = $sum(-3, $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))))),
% 0.52/0.52      inference(transitivity,[status(thm)],[89, 75])).
% 0.52/0.52  tff(91,plain,
% 0.52/0.52      (($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = 0) <=> ($sum(-3, $sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x)))))) = 0)),
% 0.52/0.52      inference(monotonicity,[status(thm)],[90])).
% 0.52/0.52  tff(92,plain,
% 0.52/0.52      (($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = 0) <=> ($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3)),
% 0.52/0.52      inference(transitivity,[status(thm)],[91, 71])).
% 0.52/0.52  tff(93,axiom,($difference($sum($sum($sum($sum($product($product($product(3, x), x), y), $product($product(2, x), y)), y), $product($product(9, x), x)), $product(5, x)), 3) = 0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq3')).
% 0.52/0.52  tff(94,plain,
% 0.52/0.52      ($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[93, 92])).
% 0.52/0.52  tff(95,plain,
% 0.52/0.52      ($sum($product(3, $product(x, $product(x, y))), $sum($product(2, $product(x, y)), $sum(y, $sum($product(9, $product(x, x)), $product(5, x))))) = 3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[94, 70])).
% 0.52/0.52  tff(96,plain,
% 0.52/0.52      ($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))) = 3),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[95, 69])).
% 0.52/0.52  tff(97,plain,
% 0.52/0.52      (3 = $sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y)))))))),
% 0.52/0.52      inference(modus_ponens,[status(thm)],[96, 68])).
% 0.52/0.52  tff(98,plain,
% 0.52/0.52      ((~(3 = $sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))))) | $lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)),
% 0.52/0.52      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.52  tff(99,plain,
% 0.52/0.52      ($lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)),
% 0.52/0.52      inference(unit_resolution,[status(thm)],[98, 97])).
% 0.52/0.52  tff(100,assumption,($lesseq(y, 0)), introduced(assumption)).
% 0.52/0.52  tff(101,plain,
% 0.52/0.52      ((~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$greatereq(x, 0)) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$lesseq(y, 0)) | (~$greatereq($product(x, y), 0))),
% 0.52/0.52      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.52  tff(102,plain,
% 0.52/0.52      (~$greatereq($product(x, y), 0)),
% 0.52/0.52      inference(unit_resolution,[status(thm)],[101, 100, 99, 22, 66, 12])).
% 0.52/0.52  tff(103,assumption,($greatereq(y, 0)), introduced(assumption)).
% 0.52/0.52  tff(104,assumption,(~$greatereq($product(x, y), 0)), introduced(assumption)).
% 0.52/0.52  tff(105,plain,
% 0.52/0.52      ((~$greatereq(y, 0)) | (~$lesseq(y, 0)) | $greatereq($product(x, y), 0)),
% 0.52/0.52      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.52  tff(106,plain,
% 0.52/0.52      ($false),
% 0.52/0.52      inference(unit_resolution,[status(thm)],[105, 100, 104, 103])).
% 0.52/0.52  tff(107,plain,((~$greatereq(y, 0)) | (~$lesseq(y, 0)) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(108,plain,
% 0.52/0.53      (~$greatereq(y, 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[107, 100, 102])).
% 0.52/0.53  tff(109,assumption,(~$greatereq($product(x, $product(x, x)), 0)), introduced(assumption)).
% 0.52/0.53  tff(110,assumption,($greatereq(x, 0)), introduced(assumption)).
% 0.52/0.53  tff(111,plain,
% 0.52/0.53      ((~$greatereq(x, 0)) | $greatereq($product(x, $product(x, x)), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(112,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[111, 110, 109])).
% 0.52/0.53  tff(113,plain,((~$greatereq(x, 0)) | $greatereq($product(x, $product(x, x)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(114,plain,
% 0.52/0.53      ($greatereq($product(x, $product(x, x)), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[113, 22])).
% 0.52/0.53  tff(115,assumption,($greatereq($product(x, $product(x, $product(x, y))), 0)), introduced(assumption)).
% 0.52/0.53  tff(116,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[115, 17, 114, 100, 99, 12, 66])).
% 0.52/0.53  tff(117,plain,((~$greatereq($product(x, $product(x, $product(x, y))), 0)) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$lesseq(y, 0))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(118,plain,
% 0.52/0.53      (~$greatereq($product(x, $product(x, $product(x, y))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[117, 100, 17])).
% 0.52/0.53  tff(119,assumption,(~$greatereq($product(x, $product(x, $product(x, y))), 0)), introduced(assumption)).
% 0.52/0.53  tff(120,assumption,(~$greatereq(x, 1)), introduced(assumption)).
% 0.52/0.53  tff(121,assumption,(~$greatereq(y, 0)), introduced(assumption)).
% 0.52/0.53  tff(122,assumption,($greatereq(y, -2)), introduced(assumption)).
% 0.52/0.53  tff(123,plain,
% 0.52/0.53      ($greatereq(x, 1) | (~$greatereq(y, -2)) | $greatereq(y, 0) | $greatereq($product(x, y), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(124,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[123, 104, 121, 120, 122])).
% 0.52/0.53  tff(125,plain,($greatereq(x, 1) | $greatereq($product(x, y), 0) | $greatereq(y, 0) | (~$greatereq(y, -2))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(126,plain,
% 0.52/0.53      (~$greatereq(y, -2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[125, 120, 121, 104])).
% 0.52/0.53  tff(127,assumption,(~$greatereq(y, -2)), introduced(assumption)).
% 0.52/0.53  tff(128,plain,
% 0.52/0.53      ($greatereq(x, 1) | $greatereq(y, -2) | $greatereq($product(x, $product(x, $product(x, y))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(129,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[128, 119, 120, 127])).
% 0.52/0.53  tff(130,plain,($greatereq(x, 1) | $greatereq($product(x, $product(x, $product(x, y))), 0) | $greatereq(y, -2)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(131,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[130, 126, 120, 119])).
% 0.52/0.53  tff(132,plain,($greatereq(x, 1) | $greatereq($product(x, $product(x, $product(x, y))), 0) | $greatereq(y, 0) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(133,plain,
% 0.52/0.53      ($greatereq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[132, 118, 108, 102])).
% 0.52/0.53  tff(134,plain,
% 0.52/0.53      ((~$lesseq(x, 0)) | (~$greatereq(x, 1))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(135,plain,
% 0.52/0.53      (~$lesseq(x, 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[134, 133])).
% 0.52/0.53  tff(136,assumption,(~$lesseq($product(x, $product(x, y)), 0)), introduced(assumption)).
% 0.52/0.53  tff(137,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), 0) | $greatereq(y, 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(138,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[137, 136, 121])).
% 0.52/0.53  tff(139,plain,($lesseq($product(x, $product(x, y)), 0) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(140,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[139, 108])).
% 0.52/0.53  tff(141,assumption,($lesseq($product(x, $product(x, y)), 0)), introduced(assumption)).
% 0.52/0.53  tff(142,assumption,(~$lesseq($product(x, x), 0)), introduced(assumption)).
% 0.52/0.53  tff(143,plain,
% 0.52/0.53      ($greatereq(x, 1) | $lesseq($product(x, x), 0) | (~$greatereq(x, 0))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(144,plain,
% 0.52/0.53      ($greatereq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[143, 22, 142])).
% 0.52/0.53  tff(145,plain,
% 0.52/0.53      ($greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0) | (~$greatereq(x, 1)) | (~$lesseq($product(x, $product(x, y)), 0))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(146,plain,
% 0.52/0.53      ($greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[145, 141, 144])).
% 0.52/0.53  tff(147,plain,
% 0.52/0.53      ((0 = $sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y))))) <=> ($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))) = 0)),
% 0.52/0.53      inference(commutativity,[status(thm)],[])).
% 0.52/0.53  tff(148,plain,
% 0.52/0.53      ((~(0 = $sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))))) <=> (~($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))) = 0))),
% 0.52/0.53      inference(monotonicity,[status(thm)],[147])).
% 0.52/0.53  tff(149,plain,
% 0.52/0.53      ((~$greatereq($product(x, $product(x, x)), 0)) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | $greatereq(y, 0) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$greatereq($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))), 0))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(150,plain,
% 0.52/0.53      (~$greatereq($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[149, 121, 99, 17, 114, 66, 12])).
% 0.52/0.53  tff(151,plain,
% 0.52/0.53      ((~(0 = $sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))))) | $greatereq($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(152,plain,
% 0.52/0.53      (~(0 = $sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[151, 150])).
% 0.52/0.53  tff(153,plain,
% 0.52/0.53      (~($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))) = 0)),
% 0.52/0.53      inference(modus_ponens,[status(thm)],[152, 148])).
% 0.52/0.53  tff(154,plain,
% 0.52/0.53      ((~(y = -1)) | ($sum($product(x, $product(x, x)), $product(x, $product(x, $product(x, y)))) = 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(155,plain,
% 0.52/0.53      (~(y = -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[154, 153])).
% 0.52/0.53  tff(156,plain,
% 0.52/0.53      ($lesseq(y, -1) | $greatereq(y, 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(157,plain,
% 0.52/0.53      ($lesseq(y, -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[156, 121])).
% 0.52/0.53  tff(158,plain,
% 0.52/0.53      ((y = -1) | (~$lesseq(y, -1)) | (~$greatereq(y, -1))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(159,plain,
% 0.52/0.53      ((y = -1) | (~$greatereq(y, -1))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[158, 157])).
% 0.52/0.53  tff(160,plain,
% 0.52/0.53      (~$greatereq(y, -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[159, 155])).
% 0.52/0.53  tff(161,plain,
% 0.52/0.53      ((~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | $greatereq(y, -1) | (~$lesseq($product(x, x), 1))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(162,plain,
% 0.52/0.53      (~$lesseq($product(x, x), 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[161, 160, 99, 66, 146, 12])).
% 0.52/0.53  tff(163,plain,
% 0.52/0.53      ((~($product(x, x) = 1)) | $lesseq($product(x, x), 1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(164,plain,
% 0.52/0.53      (~($product(x, x) = 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[163, 162])).
% 0.52/0.53  tff(165,plain,
% 0.52/0.53      ($lesseq(y, -2) | $greatereq(y, -1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(166,plain,
% 0.52/0.53      ($lesseq(y, -2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[165, 160])).
% 0.52/0.53  tff(167,assumption,(~$lesseq($product(x, $product(x, y)), -1)), introduced(assumption)).
% 0.52/0.53  tff(168,plain,
% 0.52/0.53      ($lesseq($sum(x, $product(-1, $product(x, x))), 0) | (~$greatereq(x, 1)) | $lesseq($product(x, x), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(169,plain,
% 0.52/0.53      ($lesseq($sum(x, $product(-1, $product(x, x))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[168, 142, 144])).
% 0.52/0.53  tff(170,assumption,($lesseq($sum(x, $product(-1, $product(x, x))), 0)), introduced(assumption)).
% 0.52/0.53  tff(171,assumption,($lesseq(y, -2)), introduced(assumption)).
% 0.52/0.53  tff(172,assumption,(~$lesseq(x, 2)), introduced(assumption)).
% 0.52/0.53  tff(173,plain,
% 0.52/0.53      ((~$lesseq($product(x, $product(x, y)), -27)) | $lesseq($product(x, $product(x, y)), -1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(174,plain,
% 0.52/0.53      (~$lesseq($product(x, $product(x, y)), -27)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[173, 167])).
% 0.52/0.53  tff(175,assumption,(~$lesseq($product(x, $product(x, y)), -27)), introduced(assumption)).
% 0.52/0.53  tff(176,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), -27) | $lesseq(x, 2) | $greatereq(y, -2)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(177,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[176, 127, 172, 175])).
% 0.52/0.53  tff(178,plain,($lesseq($product(x, $product(x, y)), -27) | $greatereq(y, -2) | $lesseq(x, 2)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(179,plain,
% 0.52/0.53      ($greatereq(y, -2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[178, 174, 172])).
% 0.52/0.53  tff(180,plain,
% 0.52/0.53      ((y = -2) | (~$lesseq(y, -2)) | (~$greatereq(y, -2))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(181,plain,
% 0.52/0.53      ((y = -2) | (~$greatereq(y, -2))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[180, 171])).
% 0.52/0.53  tff(182,plain,
% 0.52/0.53      (y = -2),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[181, 179])).
% 0.52/0.53  tff(183,plain,
% 0.52/0.53      ((~(y = -2)) | $greatereq($sum($product(x, $product(x, y)), $product(2, $product(x, x))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(184,plain,
% 0.52/0.53      ($greatereq($sum($product(x, $product(x, y)), $product(2, $product(x, x))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[183, 182])).
% 0.52/0.53  tff(185,plain,
% 0.52/0.53      ((~(3 = $sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))))) | $greatereq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(186,plain,
% 0.52/0.53      ($greatereq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[185, 97])).
% 0.52/0.53  tff(187,plain,
% 0.52/0.53      ((~(0 = $sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))))) | $lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(188,plain,
% 0.52/0.53      ($lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[187, 10])).
% 0.52/0.53  tff(189,plain,
% 0.52/0.53      ((~(3 = $sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))))) | $lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(190,plain,
% 0.52/0.53      ($lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[189, 64])).
% 0.52/0.53  tff(191,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[190, 172, 188, 186, 179, 170, 184])).
% 0.52/0.53  tff(192,plain,($lesseq(x, 2) | (~$lesseq($sum(x, $product(-1, $product(x, x))), 0)) | (~$lesseq(y, -2)) | $lesseq($product(x, $product(x, y)), -1)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(193,plain,
% 0.52/0.53      ($lesseq(x, 2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[192, 171, 170, 167])).
% 0.52/0.53  tff(194,assumption,(~$lesseq(x, 1)), introduced(assumption)).
% 0.52/0.53  tff(195,plain,
% 0.52/0.53      ($greatereq(x, 2) | $lesseq(x, 1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(196,plain,
% 0.52/0.53      ($greatereq(x, 2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[195, 194])).
% 0.52/0.53  tff(197,plain,
% 0.52/0.53      ((x = 2) | (~$lesseq(x, 2)) | (~$greatereq(x, 2))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(198,plain,
% 0.52/0.53      ((x = 2) | (~$lesseq(x, 2))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[197, 196])).
% 0.52/0.53  tff(199,plain,
% 0.52/0.53      (x = 2),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[198, 193])).
% 0.52/0.53  tff(200,plain,
% 0.52/0.53      ((~(x = 2)) | $lesseq($sum($product(x, $product(x, x)), $product(-2, $product(x, x))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(201,plain,
% 0.52/0.53      ($lesseq($sum($product(x, $product(x, x)), $product(-2, $product(x, x))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[200, 199])).
% 0.52/0.53  tff(202,plain,
% 0.52/0.53      ((~(x = 2)) | $greatereq($sum($product(2, $product(x, y)), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(203,plain,
% 0.52/0.53      ($greatereq($sum($product(2, $product(x, y)), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[202, 199])).
% 0.52/0.53  tff(204,assumption,(~$greatereq(y, -1)), introduced(assumption)).
% 0.52/0.53  tff(205,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[204, 196, 12, 99, 17, 66, 203, 201])).
% 0.52/0.53  tff(206,plain,((~$lesseq(y, -2)) | $greatereq(y, -1) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$lesseq($sum(x, $product(-1, $product(x, x))), 0)) | $lesseq($product(x, $product(x, y)), -1) | $lesseq(x, 1)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(207,plain,
% 0.52/0.53      ($lesseq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[206, 160, 17, 169, 167, 166])).
% 0.52/0.53  tff(208,plain,
% 0.52/0.53      ((x = 1) | (~$lesseq(x, 1)) | (~$greatereq(x, 1))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(209,plain,
% 0.52/0.53      ((x = 1) | (~$lesseq(x, 1))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[208, 144])).
% 0.52/0.53  tff(210,plain,
% 0.52/0.53      (x = 1),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[209, 207])).
% 0.52/0.53  tff(211,plain,
% 0.52/0.53      ((~(x = 1)) | (~(x = 1)) | ($product(x, x) = 1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(212,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[211, 210, 164])).
% 0.52/0.53  tff(213,plain,($lesseq($product(x, $product(x, y)), -1) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | $greatereq(y, 0) | $lesseq($product(x, x), 0) | (~$lesseq($product(x, $product(x, y)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(214,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[213, 121, 17, 142, 141])).
% 0.52/0.53  tff(215,plain,
% 0.52/0.53      ((~$greatereq($product(x, $product(x, y)), 0)) | (~$lesseq($product(x, $product(x, y)), -1))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(216,plain,
% 0.52/0.53      (~$greatereq($product(x, $product(x, y)), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[215, 214])).
% 0.52/0.53  tff(217,assumption,(~$greatereq($product(x, $product(x, y)), 0)), introduced(assumption)).
% 0.52/0.53  tff(218,assumption,(~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)), introduced(assumption)).
% 0.52/0.53  tff(219,assumption,(~$lesseq(x, 0)), introduced(assumption)).
% 0.52/0.53  tff(220,plain,
% 0.52/0.53      ($greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0) | $lesseq(x, 0) | $greatereq($product(x, $product(x, y)), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(221,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[220, 218, 219, 217])).
% 0.52/0.53  tff(222,plain,($lesseq(x, 0) | $greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0) | $greatereq($product(x, $product(x, y)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(223,plain,
% 0.52/0.53      ($lesseq(x, 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[222, 217, 218])).
% 0.52/0.53  tff(224,plain,
% 0.52/0.53      ((~$greatereq(x, 0)) | $greatereq(y, 0) | (~$lesseq(x, 0)) | $greatereq($product(x, $product(x, y)), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(225,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[224, 110, 121, 223, 217])).
% 0.52/0.53  tff(226,plain,($greatereq($product(x, $product(x, y)), 0) | (~$greatereq(x, 0)) | $greatereq(y, 0) | $greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(227,plain,
% 0.52/0.53      ($greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[226, 121, 22, 216])).
% 0.52/0.53  tff(228,plain,
% 0.52/0.53      ((~$greatereq(x, 0)) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | $greatereq(y, 0) | (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)) | (~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(229,plain,
% 0.52/0.53      (~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[228, 121, 99, 22, 66, 227, 12])).
% 0.52/0.53  tff(230,plain,
% 0.52/0.53      ((0 = $sum($product(x, $product(x, y)), $product(x, x))) <=> ($sum($product(x, $product(x, y)), $product(x, x)) = 0)),
% 0.52/0.53      inference(commutativity,[status(thm)],[])).
% 0.52/0.53  tff(231,plain,
% 0.52/0.53      (($sum($product(x, $product(x, y)), $product(x, x)) = 0) <=> (0 = $sum($product(x, $product(x, y)), $product(x, x)))),
% 0.52/0.53      inference(symmetry,[status(thm)],[230])).
% 0.52/0.53  tff(232,assumption,(y = -1), introduced(assumption)).
% 0.52/0.53  tff(233,plain,
% 0.52/0.53      ((~(y = -1)) | ($sum($product(x, $product(x, y)), $product(x, x)) = 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(234,plain,
% 0.52/0.53      ($sum($product(x, $product(x, y)), $product(x, x)) = 0),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[233, 232])).
% 0.52/0.53  tff(235,plain,
% 0.52/0.53      (0 = $sum($product(x, $product(x, y)), $product(x, x))),
% 0.52/0.53      inference(modus_ponens,[status(thm)],[234, 231])).
% 0.52/0.53  tff(236,assumption,(~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)), introduced(assumption)).
% 0.52/0.53  tff(237,plain,
% 0.52/0.53      ((~(0 = $sum($product(x, $product(x, y)), $product(x, x)))) | $greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(238,plain,
% 0.52/0.53      (~(0 = $sum($product(x, $product(x, y)), $product(x, x)))),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[237, 236])).
% 0.52/0.53  tff(239,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[238, 235])).
% 0.52/0.53  tff(240,plain,((~(y = -1)) | $greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(241,plain,
% 0.52/0.53      (~(y = -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[240, 229])).
% 0.52/0.53  tff(242,plain,
% 0.52/0.53      (~$greatereq(y, -1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[159, 241])).
% 0.52/0.53  tff(243,plain,
% 0.52/0.53      ($lesseq(y, -2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[165, 242])).
% 0.52/0.53  tff(244,assumption,($greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)), introduced(assumption)).
% 0.52/0.53  tff(245,assumption,(~$greatereq($product(x, x), 3)), introduced(assumption)).
% 0.52/0.53  tff(246,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[244, 245, 66, 99, 12, 121])).
% 0.52/0.53  tff(247,plain,($greatereq($product(x, x), 3) | (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(248,plain,
% 0.52/0.53      ($greatereq($product(x, x), 3)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[247, 244, 121])).
% 0.52/0.53  tff(249,assumption,(x = 1), introduced(assumption)).
% 0.52/0.53  tff(250,assumption,($greatereq($product(x, x), 3)), introduced(assumption)).
% 0.52/0.53  tff(251,plain,
% 0.52/0.53      ((~(x = 1)) | (~(x = 1)) | (~$greatereq($product(x, x), 3))),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(252,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[251, 250, 249, 249])).
% 0.52/0.53  tff(253,plain,((~(x = 1)) | (~$greatereq($product(x, x), 3))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(254,plain,
% 0.52/0.53      (~(x = 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[253, 248])).
% 0.52/0.53  tff(255,plain,
% 0.52/0.53      ($greatereq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[125, 122, 121, 104])).
% 0.52/0.53  tff(256,plain,
% 0.52/0.53      (~$lesseq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[208, 255, 254])).
% 0.52/0.53  tff(257,plain,
% 0.52/0.53      (y = -2),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[180, 171, 122])).
% 0.52/0.53  tff(258,assumption,(~$greatereq($sum($product(x, $product(x, y)), $product(2, $product(x, x))), 0)), introduced(assumption)).
% 0.52/0.53  tff(259,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[183, 258, 257])).
% 0.52/0.53  tff(260,plain,($greatereq($sum($product(x, $product(x, y)), $product(2, $product(x, x))), 0) | (~$lesseq(y, -2)) | (~$greatereq(y, -2))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(261,plain,
% 0.52/0.53      ($greatereq($sum($product(x, $product(x, y)), $product(2, $product(x, x))), 0)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[260, 122, 171])).
% 0.52/0.53  tff(262,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[244, 188, 261, 122, 256, 190])).
% 0.52/0.53  tff(263,plain,((~$greatereq(y, -2)) | (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)) | (~$lesseq(y, -2)) | $greatereq(y, 0) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(264,plain,
% 0.52/0.53      (~$greatereq(y, -2)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[263, 227, 243, 121, 104])).
% 0.52/0.53  tff(265,plain,
% 0.52/0.53      ($greatereq($product(x, x), 3)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[247, 227, 121])).
% 0.52/0.53  tff(266,plain,
% 0.52/0.53      (~(x = 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[253, 265])).
% 0.52/0.53  tff(267,plain,
% 0.52/0.53      ($greatereq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[130, 264, 119])).
% 0.52/0.53  tff(268,plain,
% 0.52/0.53      (~$lesseq(x, 1)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[208, 267, 266])).
% 0.52/0.53  tff(269,assumption,(~$lesseq($product(x, $product(x, y)), -12)), introduced(assumption)).
% 0.52/0.53  tff(270,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), -12) | $greatereq(y, -2) | $lesseq(x, 1)),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.52/0.53  tff(271,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[270, 194, 127, 269])).
% 0.52/0.53  tff(272,plain,($lesseq($product(x, $product(x, y)), -12) | $lesseq(x, 1) | $greatereq(y, -2)), inference(lemma,lemma(discharge,[]))).
% 0.52/0.53  tff(273,plain,
% 0.52/0.53      ($lesseq($product(x, $product(x, y)), -12)),
% 0.52/0.53      inference(unit_resolution,[status(thm)],[272, 194, 127])).
% 0.52/0.53  tff(274,assumption,(~$greatereq(x, 3)), introduced(assumption)).
% 0.52/0.53  tff(275,assumption,(~$greatereq($product(x, x), 6)), introduced(assumption)).
% 0.52/0.53  tff(276,assumption,($lesseq($product(x, $product(x, y)), -12)), introduced(assumption)).
% 0.52/0.53  tff(277,plain,
% 0.52/0.53      ($false),
% 0.52/0.53      inference(theory_lemma,[status(thm)],[99, 276, 274, 127, 275, 12, 66])).
% 0.52/0.53  tff(278,plain,($greatereq($product(x, x), 6) | (~$lesseq($product(x, $product(x, y)), -12)) | $greatereq(x, 3) | $greatereq(y, -2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.53  tff(279,plain,
% 0.54/0.53      ($greatereq($product(x, x), 6)),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[278, 274, 273, 127])).
% 0.54/0.53  tff(280,plain,
% 0.54/0.53      ((~$greatereq($product(x, x), 6)) | $greatereq(x, 3) | $lesseq(x, 1)),
% 0.54/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.53  tff(281,plain,
% 0.54/0.53      ($false),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[280, 194, 274, 279])).
% 0.54/0.53  tff(282,plain,($greatereq(x, 3) | $lesseq(x, 1) | $greatereq(y, -2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.53  tff(283,plain,
% 0.54/0.53      ($greatereq(x, 3)),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[282, 268, 264])).
% 0.54/0.53  tff(284,plain,
% 0.54/0.53      ((~$greatereq(x, 3)) | (~$lesseq(x, 2))),
% 0.54/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.53  tff(285,plain,
% 0.54/0.53      (~$lesseq(x, 2)),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[284, 283])).
% 0.54/0.53  tff(286,plain,
% 0.54/0.53      ($lesseq($product(x, $product(x, y)), -27)),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[178, 285, 264])).
% 0.54/0.53  tff(287,assumption,($greatereq(x, 4)), introduced(assumption)).
% 0.54/0.53  tff(288,plain,
% 0.54/0.53      ((~$greatereq(x, 4)) | $greatereq(y, -2) | (~$lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0))),
% 0.54/0.53      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.53  tff(289,plain,
% 0.54/0.53      ($false),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[288, 188, 12, 127, 287])).
% 0.54/0.53  tff(290,plain,((~$greatereq(x, 4)) | $greatereq(y, -2)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.53  tff(291,plain,
% 0.54/0.53      (~$greatereq(x, 4)),
% 0.54/0.53      inference(unit_resolution,[status(thm)],[290, 264])).
% 0.54/0.53  tff(292,assumption,(~$lesseq($product(x, x), 9)), introduced(assumption)).
% 0.54/0.53  tff(293,assumption,(~$greatereq(x, 4)), introduced(assumption)).
% 0.54/0.53  tff(294,assumption,($greatereq(x, 3)), introduced(assumption)).
% 0.54/0.53  tff(295,plain,
% 0.54/0.53      ($lesseq($product(x, x), 9) | (~$greatereq(x, 3)) | $greatereq(x, 4)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(296,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[295, 294, 293, 292])).
% 0.54/0.54  tff(297,plain,($lesseq($product(x, x), 9) | (~$greatereq(x, 3)) | $greatereq(x, 4)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(298,plain,
% 0.54/0.54      ($lesseq($product(x, x), 9)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[297, 283, 291])).
% 0.54/0.54  tff(299,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[66, 298, 264, 291, 12, 286, 99])).
% 0.54/0.54  tff(300,plain,($greatereq(y, 0) | $greatereq($product(x, $product(x, $product(x, y))), 0) | $greatereq($product(x, y), 0) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | $lesseq($product(x, x), 0) | (~$lesseq($product(x, $product(x, y)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(301,plain,
% 0.54/0.54      ($lesseq($product(x, x), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[300, 140, 102, 17, 108, 118])).
% 0.54/0.54  tff(302,plain,
% 0.54/0.54      ($lesseq(x, 0) | (~$lesseq($product(x, x), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(303,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[302, 301, 135])).
% 0.54/0.54  tff(304,plain,((~$lesseq(y, 0)) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(305,plain,
% 0.54/0.54      (~$lesseq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[304, 17])).
% 0.54/0.54  tff(306,assumption,(~$lesseq(y, 0)), introduced(assumption)).
% 0.54/0.54  tff(307,plain,
% 0.54/0.54      ((~$greatereq(x, 0)) | $lesseq(y, 0) | $greatereq($product(x, $product(x, $product(x, y))), 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(308,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[307, 110, 306, 119])).
% 0.54/0.54  tff(309,plain,($greatereq($product(x, $product(x, $product(x, y))), 0) | (~$greatereq(x, 0)) | $lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(310,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, $product(x, y))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[309, 22, 305])).
% 0.54/0.54  tff(311,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0) | $lesseq(y, 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(312,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[311, 306, 217])).
% 0.54/0.54  tff(313,plain,($greatereq($product(x, $product(x, y)), 0) | $lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(314,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[313, 305])).
% 0.54/0.54  tff(315,assumption,($greatereq($product(x, x), 0)), introduced(assumption)).
% 0.54/0.54  tff(316,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[188, 315, 314, 310, 22, 17])).
% 0.54/0.54  tff(317,plain,((~$greatereq($product(x, x), 0)) | $greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(318,plain,
% 0.54/0.54      ($greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[317, 16])).
% 0.54/0.54  tff(319,plain,
% 0.54/0.54      ((0 = $sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x)))))) <=> ($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))) = 0)),
% 0.54/0.54      inference(commutativity,[status(thm)],[])).
% 0.54/0.54  tff(320,plain,
% 0.54/0.54      (($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))) = 0) <=> (0 = $sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))))),
% 0.54/0.54      inference(symmetry,[status(thm)],[319])).
% 0.54/0.54  tff(321,plain,
% 0.54/0.54      ((~($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))) = 0)) <=> (~(0 = $sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x)))))))),
% 0.54/0.54      inference(monotonicity,[status(thm)],[320])).
% 0.54/0.54  tff(322,plain,
% 0.54/0.54      ((~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0)) <=> (~($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))) = 0))),
% 0.54/0.54      inference(rewrite,[status(thm)],[])).
% 0.54/0.54  tff(323,plain,
% 0.54/0.54      ((~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0)) <=> (~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0))),
% 0.54/0.54      inference(rewrite,[status(thm)],[])).
% 0.54/0.54  tff(324,plain,
% 0.54/0.54      ((~($sum($product(2, $product($product(x, x), x)), $product(-1, $sum($product(5, x), $product(5, $product(x, x))))) = 0)) <=> (~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0))),
% 0.54/0.54      inference(rewrite,[status(thm)],[])).
% 0.54/0.54  tff(325,axiom,(~($sum($product(2, $product($product(x, x), x)), $product(-1, $sum($product(5, x), $product(5, $product(x, x))))) = 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.54/0.54  tff(326,plain,
% 0.54/0.54      (~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0)),
% 0.54/0.54      inference(modus_ponens,[status(thm)],[325, 324])).
% 0.54/0.54  tff(327,plain,
% 0.54/0.54      (~($sum($product(2, $product(x, $product(x, x))), $sum($product(-5, x), $product(-5, $product(x, x)))) = 0)),
% 0.54/0.54      inference(modus_ponens,[status(thm)],[326, 323])).
% 0.54/0.54  tff(328,plain,
% 0.54/0.54      (~($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))) = 0)),
% 0.54/0.54      inference(modus_ponens,[status(thm)],[327, 322])).
% 0.54/0.54  tff(329,plain,
% 0.54/0.54      (~(0 = $sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))))),
% 0.54/0.54      inference(modus_ponens,[status(thm)],[328, 321])).
% 0.54/0.54  tff(330,plain,
% 0.54/0.54      ((0 = $sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x)))))) | (~$lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)) | (~$greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(331,plain,
% 0.54/0.54      ((~$lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)) | (~$greatereq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0))),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[330, 329])).
% 0.54/0.54  tff(332,plain,
% 0.54/0.54      (~$lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[331, 318])).
% 0.54/0.54  tff(333,assumption,(~$lesseq($product(x, $product(x, $product(x, y))), -1)), introduced(assumption)).
% 0.54/0.54  tff(334,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, $product(x, y))), -1) | $greatereq(x, 0) | $lesseq(y, 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(335,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[334, 306, 18, 333])).
% 0.54/0.54  tff(336,plain,($lesseq($product(x, $product(x, $product(x, y))), -1) | $lesseq(y, 0) | $greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(337,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, $product(x, y))), -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[336, 18, 306])).
% 0.54/0.54  tff(338,plain,
% 0.54/0.54      ((~$lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | $lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$lesseq($product(x, $product(x, $product(x, y))), -1)) | $lesseq(y, 0) | (~$greatereq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | $greatereq(x, 0) | $lesseq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(339,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[338, 337, 186, 332, 306, 18, 190, 188])).
% 0.54/0.54  tff(340,plain,
% 0.54/0.54      ($greatereq(x, 0) | (~$lesseq($product(x, $product(x, y)), 0)) | $lesseq(y, 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(341,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[340, 306, 18, 339])).
% 0.54/0.54  tff(342,plain,($greatereq(x, 0) | $lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(343,plain,
% 0.54/0.54      ($lesseq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[342, 18])).
% 0.54/0.54  tff(344,plain,
% 0.54/0.54      ((~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$lesseq(y, 0)) | (~$greatereq($sum($product(x, y), x), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(345,plain,
% 0.54/0.54      ((~$lesseq(y, 0)) | (~$greatereq($sum($product(x, y), x), 0))),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[344, 99, 66, 12])).
% 0.54/0.54  tff(346,plain,
% 0.54/0.54      (~$greatereq($sum($product(x, y), x), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[345, 343])).
% 0.54/0.54  tff(347,plain,
% 0.54/0.54      ($lesseq(x, 0) | $greatereq(x, 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(348,plain,
% 0.54/0.54      ($lesseq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[347, 18])).
% 0.54/0.54  tff(349,assumption,($lesseq(x, 0)), introduced(assumption)).
% 0.54/0.54  tff(350,plain,
% 0.54/0.54      ((~$greatereq(x, 0)) | $lesseq(y, 0) | $greatereq($product(x, y), 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(351,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[350, 110, 306, 104])).
% 0.54/0.54  tff(352,plain,($greatereq($product(x, y), 0) | (~$greatereq(x, 0)) | $lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(353,plain,
% 0.54/0.54      (~$greatereq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[352, 306, 104])).
% 0.54/0.54  tff(354,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, $product(x, y))), -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[336, 306, 353])).
% 0.54/0.54  tff(355,plain,
% 0.54/0.54      ((~$lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | $lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$lesseq($product(x, $product(x, $product(x, y))), -1)) | $lesseq(y, 0) | (~$greatereq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | $greatereq(x, 0) | (~$greatereq($product(x, $product(x, y)), 1))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(356,plain,
% 0.54/0.54      (~$greatereq($product(x, $product(x, y)), 1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[355, 306, 186, 332, 190, 353, 188, 354])).
% 0.54/0.54  tff(357,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 1) | $greatereq(x, 0) | $lesseq(y, 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(358,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[357, 306, 353, 356])).
% 0.54/0.54  tff(359,plain,($lesseq(y, 0) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(360,plain,
% 0.54/0.54      ($lesseq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[359, 104])).
% 0.54/0.54  tff(361,plain,
% 0.54/0.54      ($greatereq($product(x, y), 0) | (~$lesseq(y, 0)) | (~$lesseq(x, 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(362,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[361, 360, 104, 349])).
% 0.54/0.54  tff(363,plain,((~$lesseq(x, 0)) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(364,plain,
% 0.54/0.54      ($greatereq($product(x, y), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[363, 348])).
% 0.54/0.54  tff(365,assumption,(~$greatereq($sum($product(x, y), x), 0)), introduced(assumption)).
% 0.54/0.54  tff(366,assumption,($lesseq(y, -1)), introduced(assumption)).
% 0.54/0.54  tff(367,assumption,($greatereq($product(x, y), 0)), introduced(assumption)).
% 0.54/0.54  tff(368,plain,
% 0.54/0.54      ($greatereq($sum($product(x, y), x), 0) | (~$lesseq(y, -1)) | (~$greatereq($product(x, y), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(369,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[368, 367, 366, 365])).
% 0.54/0.54  tff(370,plain,((~$lesseq(y, -1)) | (~$greatereq($product(x, y), 0)) | $greatereq($sum($product(x, y), x), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(371,plain,
% 0.54/0.54      (~$lesseq(y, -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[370, 364, 346])).
% 0.54/0.54  tff(372,assumption,(~$lesseq($product(x, $product(x, $product(x, y))), 0)), introduced(assumption)).
% 0.54/0.54  tff(373,assumption,(~$lesseq(y, -1)), introduced(assumption)).
% 0.54/0.54  tff(374,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, $product(x, y))), 0) | $lesseq(y, -1) | (~$lesseq(y, 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(375,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[374, 100, 373, 372])).
% 0.54/0.54  tff(376,plain,($lesseq($product(x, $product(x, $product(x, y))), 0) | (~$lesseq(y, 0)) | $lesseq(y, -1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(377,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, $product(x, y))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[376, 371, 343])).
% 0.54/0.54  tff(378,plain,
% 0.54/0.54      ($lesseq(y, -1) | (~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$greatereq($product(x, y), 0)) | $greatereq(x, 0) | $lesseq($sum($product(5, x), $sum($product(5, $product(x, x)), $product(-2, $product(x, $product(x, x))))), 0) | (~$lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$lesseq($product(x, $product(x, $product(x, y))), 0)) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(379,plain,
% 0.54/0.54      ($lesseq(y, -1) | (~$greatereq($product(x, y), 0)) | $greatereq(x, 0) | (~$lesseq($product(x, $product(x, $product(x, y))), 0)) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[378, 332, 99, 190])).
% 0.54/0.54  tff(380,plain,
% 0.54/0.54      (~$greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[379, 377, 364, 18, 371])).
% 0.54/0.54  tff(381,plain,
% 0.54/0.54      ($greatereq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[156, 371])).
% 0.54/0.54  tff(382,plain,
% 0.54/0.54      ((~$greatereq(y, 0)) | $greatereq(x, 0) | $greatereq(x, 0) | $greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(383,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[382, 18, 18, 381, 380])).
% 0.54/0.54  tff(384,plain,($greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(385,plain,
% 0.54/0.54      ((~$greatereq(x, 0)) | (~$lesseq(y, 0)) | (~$greatereq($product(x, y), 0))),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[101, 99, 66, 12])).
% 0.54/0.54  tff(386,plain,
% 0.54/0.54      (~$greatereq($product(x, y), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[385, 100, 384])).
% 0.54/0.54  tff(387,plain,
% 0.54/0.54      (~$lesseq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[363, 386])).
% 0.54/0.54  tff(388,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[120, 219])).
% 0.54/0.54  tff(389,plain,($greatereq(x, 1) | $lesseq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(390,plain,
% 0.54/0.54      ($greatereq(x, 1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[389, 387])).
% 0.54/0.54  tff(391,assumption,($lesseq(x, 1)), introduced(assumption)).
% 0.54/0.54  tff(392,assumption,($greatereq(x, 1)), introduced(assumption)).
% 0.54/0.54  tff(393,plain,
% 0.54/0.54      ((~$greatereq(x, 1)) | (~$lesseq(x, 1)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(394,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[393, 66, 392, 391])).
% 0.54/0.54  tff(395,plain,((~$lesseq(x, 1)) | (~$greatereq(x, 1))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(396,plain,
% 0.54/0.54      (~$lesseq(x, 1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[395, 390])).
% 0.54/0.54  tff(397,assumption,(~$greatereq($product(x, x), 4)), introduced(assumption)).
% 0.54/0.54  tff(398,plain,
% 0.54/0.54      ($greatereq($product(x, x), 4) | $lesseq(x, 1)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(399,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[398, 194, 397])).
% 0.54/0.54  tff(400,plain,($greatereq($product(x, x), 4) | $lesseq(x, 1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(401,plain,
% 0.54/0.54      ($greatereq($product(x, x), 4)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[400, 396])).
% 0.54/0.54  tff(402,plain,
% 0.54/0.54      ($greatereq(x, 2)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[195, 396])).
% 0.54/0.54  tff(403,plain,
% 0.54/0.54      ($greatereq(x, 3)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[282, 127, 194])).
% 0.54/0.54  tff(404,plain,
% 0.54/0.54      (~$greatereq(x, 4)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[290, 127])).
% 0.54/0.54  tff(405,plain,
% 0.54/0.54      ($lesseq($product(x, x), 9)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[297, 403, 404])).
% 0.54/0.54  tff(406,plain,
% 0.54/0.54      ((~$greatereq($product(x, x), 12)) | (~$lesseq($product(x, x), 9))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(407,plain,
% 0.54/0.54      (~$greatereq($product(x, x), 12)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[406, 405])).
% 0.54/0.54  tff(408,assumption,(~$greatereq($product(x, x), 12)), introduced(assumption)).
% 0.54/0.54  tff(409,assumption,(~$lesseq(x, 3)), introduced(assumption)).
% 0.54/0.54  tff(410,plain,
% 0.54/0.54      ($lesseq(x, 3) | $greatereq($product(x, x), 12)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(411,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[410, 409, 408])).
% 0.54/0.54  tff(412,plain,($lesseq(x, 3) | $greatereq($product(x, x), 12)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(413,plain,
% 0.54/0.54      ($lesseq(x, 3)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[412, 407])).
% 0.54/0.54  tff(414,assumption,($lesseq(x, 3)), introduced(assumption)).
% 0.54/0.54  tff(415,plain,
% 0.54/0.54      ((~$lesseq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | (~$lesseq(x, 3)) | (~$greatereq(x, 3)) | (~$lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$greatereq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$greatereq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(416,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[415, 188, 12, 66, 99, 294, 414])).
% 0.54/0.54  tff(417,plain,((~$lesseq(x, 3)) | (~$greatereq(x, 3))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(418,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[417, 413, 403])).
% 0.54/0.54  tff(419,plain,($greatereq(y, -2) | $lesseq(x, 1)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(420,plain,
% 0.54/0.54      ($greatereq(y, -2)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[419, 396])).
% 0.54/0.54  tff(421,assumption,($greatereq(x, 2)), introduced(assumption)).
% 0.54/0.54  tff(422,assumption,(~$lesseq($product(x, $product(x, y)), -9)), introduced(assumption)).
% 0.54/0.54  tff(423,assumption,($greatereq($product(x, x), 4)), introduced(assumption)).
% 0.54/0.54  tff(424,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[186, 423, 422, 122, 421, 188, 190])).
% 0.54/0.54  tff(425,plain,($lesseq($product(x, $product(x, y)), -9) | (~$greatereq($product(x, x), 4)) | (~$greatereq(y, -2)) | (~$greatereq(x, 2))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(426,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, y)), -9)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[425, 420, 402, 401])).
% 0.54/0.54  tff(427,plain,
% 0.54/0.54      (~$lesseq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[363, 104])).
% 0.54/0.54  tff(428,plain,
% 0.54/0.54      ($greatereq(x, 1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[389, 427])).
% 0.54/0.54  tff(429,plain,
% 0.54/0.54      (~$lesseq(x, 1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[395, 428])).
% 0.54/0.54  tff(430,plain,
% 0.54/0.54      ($greatereq($product(x, x), 4)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[400, 429])).
% 0.54/0.54  tff(431,plain,
% 0.54/0.54      ($greatereq(x, 0) | (~$lesseq(y, 0)) | $greatereq($product(x, y), 0)),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(432,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[431, 18, 100, 104])).
% 0.54/0.54  tff(433,plain,($greatereq($product(x, y), 0) | $greatereq(x, 0) | (~$lesseq(y, 0))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(434,plain,
% 0.54/0.54      ($greatereq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[433, 360, 104])).
% 0.54/0.54  tff(435,plain,
% 0.54/0.54      (~$greatereq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[107, 360, 104])).
% 0.54/0.54  tff(436,assumption,($greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)), introduced(assumption)).
% 0.54/0.54  tff(437,plain,
% 0.54/0.54      ((~$greatereq(x, 0)) | $greatereq(y, 0) | (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)) | (~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0))),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[228, 99, 66, 12])).
% 0.54/0.54  tff(438,plain,
% 0.54/0.54      (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[437, 434, 436, 435])).
% 0.54/0.54  tff(439,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[226, 438, 435, 434])).
% 0.54/0.54  tff(440,plain,
% 0.54/0.54      ((~$lesseq($product(x, $product(x, y)), -9)) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(441,plain,
% 0.54/0.54      (~$lesseq($product(x, $product(x, y)), -9)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[440, 439])).
% 0.54/0.54  tff(442,plain,
% 0.54/0.54      ($greatereq(x, 2)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[195, 429])).
% 0.54/0.54  tff(443,plain,
% 0.54/0.54      ((~$lesseq($product(x, $product(x, y)), -12)) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(444,plain,
% 0.54/0.54      (~$lesseq($product(x, $product(x, y)), -12)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[443, 439])).
% 0.54/0.54  tff(445,plain,
% 0.54/0.54      ($greatereq(y, -2)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[272, 429, 444])).
% 0.54/0.54  tff(446,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[425, 445, 442, 441, 430])).
% 0.54/0.54  tff(447,plain,($greatereq($product(x, y), 0) | (~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(448,plain,
% 0.54/0.54      (~$greatereq($sum($product(x, $product(x, y)), $product(x, x)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[447, 386])).
% 0.54/0.54  tff(449,plain,
% 0.54/0.54      (~(y = -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[240, 448])).
% 0.54/0.54  tff(450,plain,
% 0.54/0.54      (~$greatereq(y, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[107, 386, 100])).
% 0.54/0.54  tff(451,plain,
% 0.54/0.54      ($lesseq(y, -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[156, 450])).
% 0.54/0.54  tff(452,plain,
% 0.54/0.54      (~$greatereq(y, -1)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[158, 451, 449])).
% 0.54/0.54  tff(453,plain,
% 0.54/0.54      ($lesseq(y, -2)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[165, 452])).
% 0.54/0.54  tff(454,plain,
% 0.54/0.54      (~$greatereq($sum($product(x, y), $product(-1, $product(x, $product(x, y)))), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[263, 420, 450, 386, 453])).
% 0.54/0.54  tff(455,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[222, 454, 387])).
% 0.54/0.54  tff(456,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[440, 455, 426])).
% 0.54/0.54  tff(457,plain,(~$lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(458,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[313, 306])).
% 0.54/0.54  tff(459,plain,
% 0.54/0.54      ((~$lesseq($sum($product(2, $product(x, x)), $sum($product(3, $product(x, $product(x, x))), $sum($product(x, $product(x, $product(x, y))), $product(x, $product(x, y))))), 0)) | (~$greatereq(x, 0)) | $lesseq($product(x, x), 0) | (~$lesseq($sum($product(3, x), $sum($product(2, $product(x, x)), $sum(y, $sum($product(x, y), $sum($product(-6, $product(x, $product(x, x))), $product(-2, $product(x, $product(x, $product(x, y))))))))), 3)) | (~$greatereq($sum($product(5, x), $sum($product(9, $product(x, x)), $sum(y, $sum($product(2, $product(x, y)), $product(3, $product(x, $product(x, y))))))), 3)) | $lesseq(y, 0) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(460,plain,
% 0.54/0.54      ($lesseq($product(x, x), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[459, 458, 186, 110, 306, 190, 188])).
% 0.54/0.54  tff(461,assumption,($lesseq($product(x, x), 0)), introduced(assumption)).
% 0.54/0.54  tff(462,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[302, 461, 219])).
% 0.54/0.54  tff(463,plain,($lesseq(x, 0) | (~$lesseq($product(x, x), 0))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(464,plain,
% 0.54/0.54      ($lesseq(x, 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[463, 460])).
% 0.54/0.54  tff(465,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, y)), 0) | (~$greatereq(x, 0)) | $lesseq(y, 0) | (~$lesseq(x, 0))),
% 0.54/0.54      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.54  tff(466,plain,
% 0.54/0.54      ($false),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[465, 110, 306, 136, 464])).
% 0.54/0.54  tff(467,plain,($lesseq($product(x, $product(x, y)), 0) | (~$greatereq(x, 0)) | $lesseq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.54  tff(468,plain,
% 0.54/0.54      ($lesseq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[467, 457, 384])).
% 0.54/0.54  tff(469,assumption,($lesseq($product(x, $product(x, $product(x, y))), 0)), introduced(assumption)).
% 0.54/0.54  tff(470,plain,
% 0.54/0.54      ($greatereq($product(x, $product(x, y)), 0)),
% 0.54/0.54      inference(unit_resolution,[status(thm)],[313, 457])).
% 0.54/0.54  tff(471,plain,
% 0.54/0.54      ((~$greatereq(x, 0)) | $lesseq($product(x, x), 0) | $lesseq(y, 0) | (~$greatereq($product(x, $product(x, y)), 0))),
% 0.54/0.55      inference(unit_resolution,[status(thm)],[459, 186, 190, 188])).
% 0.54/0.55  tff(472,plain,
% 0.54/0.55      ($lesseq($product(x, x), 0)),
% 0.54/0.55      inference(unit_resolution,[status(thm)],[471, 457, 384, 470])).
% 0.54/0.55  tff(473,plain,
% 0.54/0.55      ($lesseq(x, 0)),
% 0.54/0.55      inference(unit_resolution,[status(thm)],[463, 472])).
% 0.54/0.55  tff(474,plain,
% 0.54/0.55      ($false),
% 0.54/0.55      inference(theory_lemma,[status(thm)],[472, 473, 469, 468, 332, 12])).
% 0.54/0.55  tff(475,plain,(~$lesseq($product(x, $product(x, $product(x, y))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.55  tff(476,plain,
% 0.54/0.55      ((~$greatereq(x, 0)) | $lesseq($product(x, $product(x, $product(x, y))), 0) | (~$lesseq(x, 0))),
% 0.54/0.55      inference(theory_lemma,[status(thm)],[])).
% 0.54/0.55  tff(477,plain,
% 0.54/0.55      ($false),
% 0.54/0.55      inference(unit_resolution,[status(thm)],[476, 384, 473, 475])).
% 0.54/0.55  % SZS output end Proof
%------------------------------------------------------------------------------