TSTP Solution File: SWW425-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW425-1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Thu Sep 29 20:58:34 EDT 2022
% Result : Unsatisfiable 0.47s 0.55s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW425-1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 16:51:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.47/0.55 % SZS status Unsatisfiable
% 0.47/0.55 % SZS output start Proof
% 0.47/0.55 tff(heap_type, type, (
% 0.47/0.55 heap: $i > $o)).
% 0.47/0.55 tff(sep_type, type, (
% 0.47/0.55 sep: ( $i * $i ) > $i)).
% 0.47/0.55 tff(emp_type, type, (
% 0.47/0.55 emp: $i)).
% 0.47/0.55 tff(lseg_type, type, (
% 0.47/0.55 lseg: ( $i * $i ) > $i)).
% 0.47/0.55 tff(x9_type, type, (
% 0.47/0.55 x9: $i)).
% 0.47/0.55 tff(x6_type, type, (
% 0.47/0.55 x6: $i)).
% 0.47/0.55 tff(x10_type, type, (
% 0.47/0.55 x10: $i)).
% 0.47/0.55 tff(x3_type, type, (
% 0.47/0.55 x3: $i)).
% 0.47/0.55 tff(x7_type, type, (
% 0.47/0.55 x7: $i)).
% 0.47/0.55 tff(x1_type, type, (
% 0.47/0.55 x1: $i)).
% 0.47/0.55 tff(x2_type, type, (
% 0.47/0.55 x2: $i)).
% 0.47/0.55 tff(x5_type, type, (
% 0.47/0.55 x5: $i)).
% 0.47/0.55 tff(1,plain,
% 0.47/0.55 (^[Sigma: $i, S: $i, T: $i] : refl((sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma))) <=> (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma))))),
% 0.47/0.55 inference(bind,[status(th)],[])).
% 0.47/0.55 tff(2,plain,
% 0.47/0.55 (![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma))) <=> ![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))),
% 0.47/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.55 tff(3,plain,
% 0.47/0.55 (![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma))) <=> ![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(4,axiom,(![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax','associative_commutative')).
% 0.47/0.55 tff(5,plain,
% 0.47/0.55 (![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.47/0.55 tff(6,plain,(
% 0.47/0.55 ![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))),
% 0.47/0.55 inference(skolemize,[status(sab)],[5])).
% 0.47/0.55 tff(7,plain,
% 0.47/0.55 (![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))),
% 0.47/0.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.47/0.55 tff(8,plain,
% 0.47/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(9,plain,
% 0.47/0.55 (sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.47/0.55 tff(10,plain,
% 0.47/0.55 (sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.47/0.55 inference(symmetry,[status(thm)],[9])).
% 0.47/0.55 tff(11,plain,
% 0.47/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.47/0.55 inference(quant_inst,[status(thm)],[])).
% 0.47/0.55 tff(12,plain,
% 0.47/0.55 (sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.47/0.55 tff(13,plain,
% 0.47/0.55 (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[12])).
% 0.47/0.55 tff(14,plain,
% 0.47/0.55 (sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.47/0.55 inference(symmetry,[status(thm)],[13])).
% 0.51/0.55 tff(15,plain,
% 0.51/0.55 (sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(monotonicity,[status(thm)],[14])).
% 0.51/0.55 tff(16,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(17,plain,
% 0.51/0.55 (sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[16, 7])).
% 0.51/0.55 tff(18,plain,
% 0.51/0.55 (sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[17])).
% 0.51/0.55 tff(19,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(20,plain,
% 0.51/0.55 (sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[19, 7])).
% 0.51/0.55 tff(21,plain,
% 0.51/0.55 (sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[20])).
% 0.51/0.55 tff(22,plain,
% 0.51/0.55 (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(monotonicity,[status(thm)],[21])).
% 0.51/0.55 tff(23,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(24,plain,
% 0.51/0.55 (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[23, 7])).
% 0.51/0.55 tff(25,plain,
% 0.51/0.55 (sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[24])).
% 0.51/0.55 tff(26,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))) = sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(27,plain,
% 0.51/0.55 (sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))) = sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.51/0.55 tff(28,plain,
% 0.51/0.55 (sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x2, x10), sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(monotonicity,[status(thm)],[27])).
% 0.51/0.55 tff(29,plain,
% 0.51/0.55 (sep(lseg(x2, x10), sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[28])).
% 0.51/0.55 tff(30,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x10), sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(31,plain,
% 0.51/0.55 (sep(lseg(x2, x10), sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[30, 7])).
% 0.51/0.55 tff(32,plain,
% 0.51/0.55 (sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x2, x10), sep(lseg(x7, x6), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[31])).
% 0.51/0.55 tff(33,plain,
% 0.51/0.55 (sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.55 inference(transitivity,[status(thm)],[32, 29])).
% 0.51/0.55 tff(34,plain,
% 0.51/0.55 (sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(monotonicity,[status(thm)],[33])).
% 0.51/0.55 tff(35,plain,
% 0.51/0.55 (sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(monotonicity,[status(thm)],[34])).
% 0.51/0.55 tff(36,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.55 inference(quant_inst,[status(thm)],[])).
% 0.51/0.55 tff(37,plain,
% 0.51/0.55 (sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(unit_resolution,[status(thm)],[36, 7])).
% 0.51/0.55 tff(38,plain,
% 0.51/0.55 (sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.55 inference(symmetry,[status(thm)],[37])).
% 0.51/0.55 tff(39,assumption,(~(x2 = x1)), introduced(assumption)).
% 0.51/0.55 tff(40,plain,
% 0.51/0.55 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x2, x5), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(quant_inst,[status(thm)],[])).
% 0.51/0.56 tff(41,plain,
% 0.51/0.56 (sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x2, x5), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[40, 7])).
% 0.51/0.56 tff(42,plain,
% 0.51/0.56 (sep(lseg(x2, x5), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(symmetry,[status(thm)],[41])).
% 0.51/0.56 tff(43,plain,
% 0.51/0.56 (sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[20])).
% 0.51/0.56 tff(44,plain,
% 0.51/0.56 (sep(lseg(x5, x7), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(symmetry,[status(thm)],[43])).
% 0.51/0.56 tff(45,plain,
% 0.51/0.56 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x5, x7), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(quant_inst,[status(thm)],[])).
% 0.51/0.56 tff(46,plain,
% 0.51/0.56 (sep(lseg(x5, x7), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[45, 7])).
% 0.51/0.56 tff(47,plain,
% 0.51/0.56 (sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x1), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(symmetry,[status(thm)],[46])).
% 0.51/0.56 tff(48,plain,
% 0.51/0.56 (sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(transitivity,[status(thm)],[47, 44])).
% 0.51/0.56 tff(49,plain,
% 0.51/0.56 (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x2, x5), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[48])).
% 0.51/0.56 tff(50,plain,
% 0.51/0.56 (sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(transitivity,[status(thm)],[49, 42])).
% 0.51/0.56 tff(51,plain,
% 0.51/0.56 (heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[50])).
% 0.51/0.56 tff(52,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(symmetry,[status(thm)],[51])).
% 0.51/0.56 tff(53,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(rewrite,[status(thm)],[])).
% 0.51/0.56 tff(54,axiom,(heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_12')).
% 0.51/0.56 tff(55,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.51/0.56 tff(56,plain,
% 0.51/0.56 (heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.51/0.56 tff(57,plain,
% 0.51/0.56 (^[Sigma: $i, Z: $i, Y: $i, X: $i] : refl(((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma))))) <=> ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma))))))),
% 0.51/0.56 inference(bind,[status(th)],[])).
% 0.51/0.56 tff(58,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma))))) <=> ![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(quant_intro,[status(thm)],[57])).
% 0.51/0.56 tff(59,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma))))) <=> ![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(rewrite,[status(thm)],[])).
% 0.51/0.56 tff(60,plain,
% 0.51/0.56 (^[Sigma: $i, Z: $i, Y: $i, X: $i] : rewrite((((~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))) | (X = Y)) | (X = Z)) <=> ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma))))))),
% 0.51/0.56 inference(bind,[status(th)],[])).
% 0.51/0.56 tff(61,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : (((~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))) | (X = Y)) | (X = Z)) <=> ![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(quant_intro,[status(thm)],[60])).
% 0.51/0.56 tff(62,axiom,(![Sigma: $i, Z: $i, Y: $i, X: $i] : (((~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))) | (X = Y)) | (X = Z))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV013-0.ax','wellformedness_5')).
% 0.51/0.56 tff(63,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.51/0.56 tff(64,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.51/0.56 tff(65,plain,(
% 0.51/0.56 ![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(skolemize,[status(sab)],[64])).
% 0.51/0.56 tff(66,plain,
% 0.51/0.56 (![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.51/0.56 tff(67,plain,
% 0.51/0.56 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x2 = x1) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x2 = x1) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.56 inference(rewrite,[status(thm)],[])).
% 0.51/0.56 tff(68,plain,
% 0.51/0.56 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x2 = x1) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.56 inference(quant_inst,[status(thm)],[])).
% 0.51/0.56 tff(69,plain,
% 0.51/0.56 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x2 = x1) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.51/0.56 tff(70,plain,
% 0.51/0.56 ((x2 = x1) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[69, 66])).
% 0.51/0.56 tff(71,plain,
% 0.51/0.56 ((x2 = x1) | (x2 = x5)),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.51/0.56 tff(72,plain,
% 0.51/0.56 (x2 = x5),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[71, 39])).
% 0.51/0.56 tff(73,plain,
% 0.51/0.56 (x5 = x2),
% 0.51/0.56 inference(symmetry,[status(thm)],[72])).
% 0.51/0.56 tff(74,plain,
% 0.51/0.56 (lseg(x5, x1) = lseg(x2, x1)),
% 0.51/0.56 inference(monotonicity,[status(thm)],[73])).
% 0.51/0.56 tff(75,plain,
% 0.51/0.56 (sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x1), sep(lseg(x2, x5), sep(lseg(x7, x6), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[74, 38])).
% 0.51/0.56 tff(76,plain,
% 0.51/0.56 (sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(transitivity,[status(thm)],[75, 35, 25, 22])).
% 0.51/0.56 tff(77,plain,
% 0.51/0.56 (sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[76])).
% 0.51/0.56 tff(78,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[77])).
% 0.51/0.56 tff(79,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(symmetry,[status(thm)],[78])).
% 0.51/0.56 tff(80,plain,
% 0.51/0.56 (heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[55, 79])).
% 0.51/0.56 tff(81,plain,
% 0.51/0.56 ((x5 = x1) <=> (x2 = x1)),
% 0.51/0.56 inference(monotonicity,[status(thm)],[73])).
% 0.51/0.56 tff(82,plain,
% 0.51/0.56 ((x2 = x1) <=> (x5 = x1)),
% 0.51/0.56 inference(symmetry,[status(thm)],[81])).
% 0.51/0.56 tff(83,plain,
% 0.51/0.56 ((~(x2 = x1)) <=> (~(x5 = x1))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[82])).
% 0.51/0.56 tff(84,plain,
% 0.51/0.56 (~(x5 = x1)),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[39, 83])).
% 0.51/0.56 tff(85,plain,
% 0.51/0.56 ((x5 = x7) <=> (x2 = x7)),
% 0.51/0.56 inference(monotonicity,[status(thm)],[73])).
% 0.51/0.56 tff(86,plain,
% 0.51/0.56 ((x2 = x7) <=> (x5 = x7)),
% 0.51/0.56 inference(symmetry,[status(thm)],[85])).
% 0.51/0.56 tff(87,plain,
% 0.51/0.56 ((~(x2 = x7)) <=> (~(x5 = x7))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[86])).
% 0.51/0.56 tff(88,plain,
% 0.51/0.56 ((~(x2 = x7)) <=> (~(x2 = x7))),
% 0.51/0.56 inference(rewrite,[status(thm)],[])).
% 0.51/0.56 tff(89,axiom,(~(x2 = x7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_11')).
% 0.51/0.56 tff(90,plain,
% 0.51/0.56 (~(x2 = x7)),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.51/0.56 tff(91,plain,
% 0.51/0.56 (~(x5 = x7)),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.51/0.56 tff(92,plain,
% 0.51/0.56 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x5 = x1) | (x5 = x7) | (~heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x5 = x1) | (x5 = x7) | (~heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.56 inference(rewrite,[status(thm)],[])).
% 0.51/0.56 tff(93,plain,
% 0.51/0.56 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x5 = x1) | (x5 = x7) | (~heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.56 inference(quant_inst,[status(thm)],[])).
% 0.51/0.56 tff(94,plain,
% 0.51/0.56 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x5 = x1) | (x5 = x7) | (~heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.56 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.51/0.56 tff(95,plain,
% 0.51/0.56 ((x5 = x1) | (x5 = x7) | (~heap(sep(lseg(x5, x7), sep(lseg(x5, x1), sep(lseg(x7, x6), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[94, 66])).
% 0.51/0.56 tff(96,plain,
% 0.51/0.56 ($false),
% 0.51/0.56 inference(unit_resolution,[status(thm)],[95, 91, 84, 80])).
% 0.51/0.56 tff(97,plain,(x2 = x1), inference(lemma,lemma(discharge,[]))).
% 0.51/0.56 tff(98,plain,
% 0.51/0.56 (x1 = x2),
% 0.51/0.56 inference(symmetry,[status(thm)],[97])).
% 0.51/0.56 tff(99,plain,
% 0.51/0.56 (lseg(x1, x10) = lseg(x2, x10)),
% 0.51/0.56 inference(monotonicity,[status(thm)],[98])).
% 0.51/0.56 tff(100,plain,
% 0.51/0.56 (sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x2, x5), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[99, 18])).
% 0.51/0.56 tff(101,plain,
% 0.51/0.56 (sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.56 inference(transitivity,[status(thm)],[100, 15, 10])).
% 0.51/0.56 tff(102,plain,
% 0.51/0.56 ((x2 = x10) <=> (x1 = x10)),
% 0.51/0.56 inference(monotonicity,[status(thm)],[97])).
% 0.51/0.56 tff(103,plain,
% 0.51/0.56 ((x1 = x10) <=> (x2 = x10)),
% 0.51/0.56 inference(symmetry,[status(thm)],[102])).
% 0.51/0.56 tff(104,plain,
% 0.51/0.56 ((~(x1 = x10)) <=> (~(x2 = x10))),
% 0.51/0.56 inference(monotonicity,[status(thm)],[103])).
% 0.51/0.57 tff(105,plain,
% 0.51/0.57 ((~(x1 = x10)) <=> (~(x1 = x10))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(106,axiom,(~(x1 = x10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_3')).
% 0.51/0.57 tff(107,plain,
% 0.51/0.57 (~(x1 = x10)),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.51/0.57 tff(108,plain,
% 0.51/0.57 (~(x2 = x10)),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[107, 104])).
% 0.51/0.57 tff(109,plain,
% 0.51/0.57 (sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))) = sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))),
% 0.51/0.57 inference(symmetry,[status(thm)],[12])).
% 0.51/0.57 tff(110,plain,
% 0.51/0.57 (sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))) = sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[109])).
% 0.51/0.57 tff(111,plain,
% 0.51/0.57 (sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[110])).
% 0.51/0.57 tff(112,plain,
% 0.51/0.57 ((~![Sigma: $i, S: $i, T: $i] : (sep(S, sep(T, Sigma)) = sep(T, sep(S, Sigma)))) | (sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.57 inference(quant_inst,[status(thm)],[])).
% 0.51/0.57 tff(113,plain,
% 0.51/0.57 (sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[112, 7])).
% 0.51/0.57 tff(114,plain,
% 0.51/0.57 (sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.57 inference(symmetry,[status(thm)],[113])).
% 0.51/0.57 tff(115,plain,
% 0.51/0.57 (sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))) = sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))),
% 0.51/0.57 inference(transitivity,[status(thm)],[114, 111])).
% 0.51/0.57 tff(116,plain,
% 0.51/0.57 (sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x2, x5), sep(lseg(x5, x7), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[115])).
% 0.51/0.57 tff(117,plain,
% 0.51/0.57 (sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.57 inference(transitivity,[status(thm)],[116, 42])).
% 0.51/0.57 tff(118,plain,
% 0.51/0.57 (heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[117])).
% 0.51/0.57 tff(119,plain,
% 0.51/0.57 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(symmetry,[status(thm)],[118])).
% 0.51/0.57 tff(120,plain,
% 0.51/0.57 (heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[55, 119])).
% 0.51/0.57 tff(121,plain,
% 0.51/0.57 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x2 = x10) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x2 = x10) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(122,plain,
% 0.51/0.57 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x2 = x10) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(quant_inst,[status(thm)],[])).
% 0.51/0.57 tff(123,plain,
% 0.51/0.57 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x2 = x10) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.51/0.57 tff(124,plain,
% 0.51/0.57 ((x2 = x10) | (x2 = x5) | (~heap(sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x5, x7), sep(lseg(x9, x1), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[123, 66])).
% 0.51/0.57 tff(125,plain,
% 0.51/0.57 ((x2 = x10) | (x2 = x5)),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[124, 120])).
% 0.51/0.57 tff(126,plain,
% 0.51/0.57 (x2 = x5),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[125, 108])).
% 0.51/0.57 tff(127,plain,
% 0.51/0.57 (x5 = x2),
% 0.51/0.57 inference(symmetry,[status(thm)],[126])).
% 0.51/0.57 tff(128,plain,
% 0.51/0.57 (lseg(x5, x7) = lseg(x2, x7)),
% 0.51/0.57 inference(monotonicity,[status(thm)],[127])).
% 0.51/0.57 tff(129,plain,
% 0.51/0.57 (lseg(x2, x7) = lseg(x5, x7)),
% 0.51/0.57 inference(symmetry,[status(thm)],[128])).
% 0.51/0.57 tff(130,plain,
% 0.51/0.57 (lseg(x1, x7) = lseg(x2, x7)),
% 0.51/0.57 inference(monotonicity,[status(thm)],[98])).
% 0.51/0.57 tff(131,plain,
% 0.51/0.57 (lseg(x1, x7) = lseg(x5, x7)),
% 0.51/0.57 inference(transitivity,[status(thm)],[130, 129])).
% 0.51/0.57 tff(132,plain,
% 0.51/0.57 (sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))) = sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[131, 101])).
% 0.51/0.57 tff(133,plain,
% 0.51/0.57 (heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[132])).
% 0.51/0.57 tff(134,plain,
% 0.51/0.57 (heap(sep(lseg(x5, x7), sep(lseg(x2, x5), sep(lseg(x2, x10), sep(lseg(x2, x1), sep(lseg(x9, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))) <=> heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(symmetry,[status(thm)],[133])).
% 0.51/0.57 tff(135,plain,
% 0.51/0.57 (heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[55, 134])).
% 0.51/0.57 tff(136,plain,
% 0.51/0.57 ((~(x1 = x7)) <=> (~(x1 = x7))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(137,axiom,(~(x1 = x7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_2')).
% 0.51/0.57 tff(138,plain,
% 0.51/0.57 (~(x1 = x7)),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.51/0.57 tff(139,plain,
% 0.51/0.57 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(140,plain,
% 0.51/0.57 (((x1 = x10) | (x1 = x7) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))) <=> ((x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(rewrite,[status(thm)],[])).
% 0.51/0.57 tff(141,plain,
% 0.51/0.57 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x1 = x10) | (x1 = x7) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[140])).
% 0.51/0.57 tff(142,plain,
% 0.51/0.57 (((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x1 = x10) | (x1 = x7) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))) <=> ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(transitivity,[status(thm)],[141, 139])).
% 0.51/0.57 tff(143,plain,
% 0.51/0.57 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | ((x1 = x10) | (x1 = x7) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))))),
% 0.51/0.57 inference(quant_inst,[status(thm)],[])).
% 0.51/0.57 tff(144,plain,
% 0.51/0.57 ((~![Sigma: $i, Z: $i, Y: $i, X: $i] : ((X = Z) | (X = Y) | (~heap(sep(lseg(X, Y), sep(lseg(X, Z), Sigma)))))) | (x1 = x7) | (x1 = x10) | (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp))))))))))),
% 0.51/0.57 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.51/0.57 tff(145,plain,
% 0.51/0.57 (~heap(sep(lseg(x1, x7), sep(lseg(x1, x10), sep(lseg(x9, x1), sep(lseg(x2, x5), sep(lseg(x2, x1), sep(lseg(x7, x6), sep(lseg(x3, x10), sep(lseg(x6, x9), emp)))))))))),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[144, 66, 138, 107])).
% 0.51/0.57 tff(146,plain,
% 0.51/0.57 ($false),
% 0.51/0.57 inference(unit_resolution,[status(thm)],[145, 135])).
% 0.51/0.57 % SZS output end Proof
%------------------------------------------------------------------------------