TSTP Solution File: ARI758_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI758_1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 17:02:52 EDT 2022
% Result : Unsatisfiable 1.59s 1.28s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI758_1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 02:25:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.59/1.28 % SZS status Unsatisfiable
% 1.59/1.28 % SZS output start Proof
% 1.59/1.28 tff(integer_of_int32_type, type, (
% 1.59/1.28 integer_of_int32: c_sorted > $int)).
% 1.59/1.28 tff(c_sort_type, type, (
% 1.59/1.28 c_sort: ( c_type * c_unsorted ) > c_sorted)).
% 1.59/1.28 tff(tptp_fun_A__questionmark_result0_305_type, type, (
% 1.59/1.28 tptp_fun_A__questionmark_result0_305: c_unsorted)).
% 1.59/1.28 tff(int32_type, type, (
% 1.59/1.28 int32: c_type)).
% 1.59/1.28 tff(tptp_fun_A__questionmark_x_304_type, type, (
% 1.59/1.28 tptp_fun_A__questionmark_x_304: c_unsorted)).
% 1.59/1.28 tff(tptp_fun_A__questionmark_x0_306_type, type, (
% 1.59/1.28 tptp_fun_A__questionmark_x0_306: c_unsorted)).
% 1.59/1.28 tff(tptp_fun_A__questionmark_result_303_type, type, (
% 1.59/1.28 tptp_fun_A__questionmark_result_303: c_unsorted)).
% 1.59/1.28 tff(c_Boolean_true_type, type, (
% 1.59/1.28 c_Boolean_true: c_Boolean)).
% 1.59/1.28 tff(1,plain,
% 1.59/1.28 ((-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305))))) <=> ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)),
% 1.59/1.28 inference(commutativity,[status(thm)],[])).
% 1.59/1.28 tff(2,plain,
% 1.59/1.28 (($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1) <=> (-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))))),
% 1.59/1.28 inference(symmetry,[status(thm)],[1])).
% 1.59/1.28 tff(3,plain,
% 1.59/1.28 ((~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)) <=> (~(-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305))))))),
% 1.59/1.28 inference(monotonicity,[status(thm)],[2])).
% 1.59/1.28 tff(4,plain,
% 1.59/1.28 (^[A__questionmark_v_0_288: c_sorted] : refl(((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(bind,[status(th)],[])).
% 1.59/1.28 tff(5,plain,
% 1.59/1.28 (![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(quant_intro,[status(thm)],[4])).
% 1.59/1.28 tff(6,plain,
% 1.59/1.28 (^[A__questionmark_v_0_288: c_sorted] : trans(monotonicity(rewrite(((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))) <=> (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))), ((~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> (~(~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))))), rewrite((~(~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))) <=> ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))), ((~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))))),
% 1.59/1.28 inference(bind,[status(th)],[])).
% 1.59/1.28 tff(7,plain,
% 1.59/1.28 (![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(quant_intro,[status(thm)],[6])).
% 1.59/1.28 tff(8,plain,
% 1.59/1.28 (((integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1) & ((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))) <=> ((integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1) & (c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(9,plain,
% 1.59/1.28 (((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & ((integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))) <=> ((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(10,plain,
% 1.59/1.28 (((~(~(integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2))) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) <=> ((integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(11,plain,
% 1.59/1.28 ((~(~(c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)))) <=> (c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(12,plain,
% 1.59/1.28 (((~(~(c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)))) & ((~(~(integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2))) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))) <=> ((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & ((integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))))),
% 1.59/1.28 inference(monotonicity,[status(thm)],[11, 10])).
% 1.59/1.28 tff(13,plain,
% 1.59/1.28 (((~(~(c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)))) & ((~(~(integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2))) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))) <=> ((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(transitivity,[status(thm)],[12, 9])).
% 1.59/1.28 tff(14,plain,
% 1.59/1.28 ((~(~(integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1))) <=> (integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1)),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(15,plain,
% 1.59/1.28 (((~(~(integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1))) & ((~(~(c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)))) & ((~(~(integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2))) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))))) <=> ((integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1) & ((c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))))),
% 1.59/1.28 inference(monotonicity,[status(thm)],[14, 13])).
% 1.59/1.28 tff(16,plain,
% 1.59/1.28 (((~(~(integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1))) & ((~(~(c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)))) & ((~(~(integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2))) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))))) <=> ((integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1) & (c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))))),
% 1.59/1.28 inference(transitivity,[status(thm)],[15, 8])).
% 1.59/1.28 tff(17,plain,
% 1.59/1.28 ((~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1))))))) <=> (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1)))))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(18,plain,
% 1.59/1.28 ((~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x)), $product(-1, integer_of_int32(A__questionmark_v_0_288))) = -1))))))) <=> (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1)))))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(19,plain,
% 1.59/1.28 ((~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))) <=> (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x)), $product(-1, integer_of_int32(A__questionmark_v_0_288))) = -1)))))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(20,plain,
% 1.59/1.28 ((~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))) <=> (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288)))))))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(21,plain,
% 1.59/1.28 ((~((c_Boolean_true = c_Boolean_true) => ![A__questionmark_result: c_unsorted] : ((integer_of_int32(c_sort(int32, A__questionmark_result)) = 1) => ![A__questionmark_x: c_unsorted] : ((c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result)) => ![A__questionmark_result0: c_unsorted] : ((integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2) => ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0)) => (integer_of_int32(c_sort(int32, A__questionmark_x)) = $difference(integer_of_int32(A__questionmark_v_0_288), 1))))))))) <=> (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288)))))))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(22,axiom,(~((c_Boolean_true = c_Boolean_true) => ![A__questionmark_result: c_unsorted] : ((integer_of_int32(c_sort(int32, A__questionmark_result)) = 1) => ![A__questionmark_x: c_unsorted] : ((c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result)) => ![A__questionmark_result0: c_unsorted] : ((integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2) => ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0)) => (integer_of_int32(c_sort(int32, A__questionmark_x)) = $difference(integer_of_int32(A__questionmark_v_0_288), 1))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','formula_170')).
% 1.59/1.28 tff(23,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.59/1.28 tff(24,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[23, 20])).
% 1.59/1.28 tff(25,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.59/1.28 tff(26,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | (integer_of_int32(c_sort(int32, A__questionmark_x)) = $sum(-1, integer_of_int32(A__questionmark_v_0_288))))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[25, 20])).
% 1.59/1.28 tff(27,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x)), $product(-1, integer_of_int32(A__questionmark_v_0_288))) = -1))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[26, 19])).
% 1.59/1.28 tff(28,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[27, 18])).
% 1.59/1.28 tff(29,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[28, 17])).
% 1.59/1.28 tff(30,plain,
% 1.59/1.28 (~![A__questionmark_result: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result)) = 1)) | ![A__questionmark_x: c_unsorted] : ((~(c_sort(int32, A__questionmark_x) = c_sort(int32, A__questionmark_result))) | ![A__questionmark_result0: c_unsorted] : ((~(integer_of_int32(c_sort(int32, A__questionmark_result0)) = 2)) | ![A__questionmark_x0: c_unsorted] : ?[A__questionmark_v_0_288: c_sorted] : ((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x)))) = 1))))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[29, 17])).
% 1.59/1.28 tff(31,plain,
% 1.59/1.28 ((integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1) & (c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)) & (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2) & ![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[30, 16])).
% 1.59/1.28 tff(32,plain,
% 1.59/1.28 (![A__questionmark_v_0_288: c_sorted] : (~((A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306)) & ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(and_elim,[status(thm)],[31])).
% 1.59/1.28 tff(33,plain,
% 1.59/1.28 (![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[32, 7])).
% 1.59/1.28 tff(34,plain,
% 1.59/1.28 (![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.28 inference(modus_ponens,[status(thm)],[33, 5])).
% 1.59/1.28 tff(35,plain,
% 1.59/1.28 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1))))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(36,plain,
% 1.59/1.28 (($false | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))) <=> (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(37,plain,
% 1.59/1.28 ((~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))) <=> (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(38,plain,
% 1.59/1.28 ((~$true) <=> $false),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(39,plain,
% 1.59/1.28 ((c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306)) <=> $true),
% 1.59/1.28 inference(rewrite,[status(thm)],[])).
% 1.59/1.28 tff(40,plain,
% 1.59/1.28 ((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) <=> (~$true)),
% 1.59/1.28 inference(monotonicity,[status(thm)],[39])).
% 1.59/1.28 tff(41,plain,
% 1.59/1.28 ((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) <=> $false),
% 1.59/1.28 inference(transitivity,[status(thm)],[40, 38])).
% 1.59/1.28 tff(42,plain,
% 1.59/1.28 (((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ($false | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1))))),
% 1.59/1.28 inference(monotonicity,[status(thm)],[41, 37])).
% 1.59/1.28 tff(43,plain,
% 1.59/1.28 (((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))),
% 1.59/1.28 inference(transitivity,[status(thm)],[42, 36])).
% 1.59/1.28 tff(44,plain,
% 1.59/1.28 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1))))),
% 1.59/1.28 inference(monotonicity,[status(thm)],[43])).
% 1.59/1.28 tff(45,plain,
% 1.59/1.28 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1))))),
% 1.59/1.28 inference(transitivity,[status(thm)],[44, 35])).
% 1.59/1.28 tff(46,plain,
% 1.59/1.28 ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x0!306)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.29 inference(quant_inst,[status(thm)],[])).
% 1.59/1.29 tff(47,plain,
% 1.59/1.29 ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)))),
% 1.59/1.29 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.59/1.29 tff(48,plain,
% 1.59/1.29 (~((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1))),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[47, 34])).
% 1.59/1.29 tff(49,plain,
% 1.59/1.29 (((~(c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x0!306)))) = -1)) | (c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305))),
% 1.59/1.29 inference(tautology,[status(thm)],[])).
% 1.59/1.29 tff(50,plain,
% 1.59/1.29 (c_sort(int32, A__questionmark_x0!306) = c_sort(int32, A__questionmark_result0!305)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.59/1.29 tff(51,plain,
% 1.59/1.29 (c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306)),
% 1.59/1.29 inference(symmetry,[status(thm)],[50])).
% 1.59/1.29 tff(52,assumption,(~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))), introduced(assumption)).
% 1.59/1.29 tff(53,plain,
% 1.59/1.29 ($false),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.59/1.29 tff(54,plain,(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.29 tff(55,plain,
% 1.59/1.29 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)))),
% 1.59/1.29 inference(rewrite,[status(thm)],[])).
% 1.59/1.29 tff(56,plain,
% 1.59/1.29 (((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1)))) <=> ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)))),
% 1.59/1.29 inference(rewrite,[status(thm)],[])).
% 1.59/1.29 tff(57,plain,
% 1.59/1.29 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1))))),
% 1.59/1.29 inference(monotonicity,[status(thm)],[56])).
% 1.59/1.29 tff(58,plain,
% 1.59/1.29 (((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) <=> ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)))),
% 1.59/1.29 inference(transitivity,[status(thm)],[57, 55])).
% 1.59/1.29 tff(59,plain,
% 1.59/1.29 ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))),
% 1.59/1.29 inference(quant_inst,[status(thm)],[])).
% 1.59/1.29 tff(60,plain,
% 1.59/1.29 ((~![A__questionmark_v_0_288: c_sorted] : ((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_x0!306))) | (~((~(A__questionmark_v_0_288 = c_sort(int32, A__questionmark_result0!305))) | ($sum(integer_of_int32(A__questionmark_v_0_288), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))) = 1))))) | (~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1))),
% 1.59/1.29 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.59/1.29 tff(61,plain,
% 1.59/1.29 ((~(c_sort(int32, A__questionmark_result0!305) = c_sort(int32, A__questionmark_x0!306))) | (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1))),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[60, 34])).
% 1.59/1.29 tff(62,plain,
% 1.59/1.29 (~($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) = -1)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[61, 54])).
% 1.59/1.29 tff(63,plain,
% 1.59/1.29 (~(-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))))),
% 1.59/1.29 inference(modus_ponens,[status(thm)],[62, 3])).
% 1.59/1.29 tff(64,plain,
% 1.59/1.29 (c_sort(int32, A__questionmark_x!304) = c_sort(int32, A__questionmark_result!303)),
% 1.59/1.29 inference(and_elim,[status(thm)],[31])).
% 1.59/1.29 tff(65,plain,
% 1.59/1.29 (integer_of_int32(c_sort(int32, A__questionmark_x!304)) = integer_of_int32(c_sort(int32, A__questionmark_result!303))),
% 1.59/1.29 inference(monotonicity,[status(thm)],[64])).
% 1.59/1.29 tff(66,plain,
% 1.59/1.29 (integer_of_int32(c_sort(int32, A__questionmark_result!303)) = integer_of_int32(c_sort(int32, A__questionmark_x!304))),
% 1.59/1.29 inference(symmetry,[status(thm)],[65])).
% 1.59/1.29 tff(67,plain,
% 1.59/1.29 ((~(integer_of_int32(c_sort(int32, A__questionmark_result!303)) = integer_of_int32(c_sort(int32, A__questionmark_x!304)))) | $lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)),
% 1.59/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.29 tff(68,plain,
% 1.59/1.29 ($lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.59/1.29 tff(69,plain,
% 1.59/1.29 (integer_of_int32(c_sort(int32, A__questionmark_result0!305)) = 2),
% 1.59/1.29 inference(and_elim,[status(thm)],[31])).
% 1.59/1.29 tff(70,plain,
% 1.59/1.29 (2 = integer_of_int32(c_sort(int32, A__questionmark_result0!305))),
% 1.59/1.29 inference(symmetry,[status(thm)],[69])).
% 1.59/1.29 tff(71,plain,
% 1.59/1.29 ((~(2 = integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) | $lesseq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)),
% 1.59/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.29 tff(72,plain,
% 1.59/1.29 ($lesseq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[71, 70])).
% 1.59/1.29 tff(73,plain,
% 1.59/1.29 (integer_of_int32(c_sort(int32, A__questionmark_result!303)) = 1),
% 1.59/1.29 inference(and_elim,[status(thm)],[31])).
% 1.59/1.29 tff(74,plain,
% 1.59/1.29 (1 = integer_of_int32(c_sort(int32, A__questionmark_result!303))),
% 1.59/1.29 inference(symmetry,[status(thm)],[73])).
% 1.59/1.29 tff(75,plain,
% 1.59/1.29 ((~(1 = integer_of_int32(c_sort(int32, A__questionmark_result!303)))) | $greatereq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)),
% 1.59/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.29 tff(76,plain,
% 1.59/1.29 ($greatereq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.59/1.29 tff(77,plain,
% 1.59/1.29 ((~$lesseq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)) | (~$greatereq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)) | (~$lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)) | $greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1)),
% 1.59/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.29 tff(78,plain,
% 1.59/1.29 ($greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1)),
% 1.59/1.29 inference(unit_resolution,[status(thm)],[77, 76, 72, 68])).
% 1.59/1.29 tff(79,plain,
% 1.59/1.29 ((~(integer_of_int32(c_sort(int32, A__questionmark_result!303)) = integer_of_int32(c_sort(int32, A__questionmark_x!304)))) | $greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)),
% 1.59/1.29 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.29 tff(80,plain,
% 1.59/1.29 ($greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[79, 66])).
% 1.59/1.30 tff(81,plain,
% 1.59/1.30 ((~(2 = integer_of_int32(c_sort(int32, A__questionmark_result0!305)))) | $greatereq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)),
% 1.59/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.30 tff(82,plain,
% 1.59/1.30 ($greatereq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[81, 70])).
% 1.59/1.30 tff(83,plain,
% 1.59/1.30 ((~(1 = integer_of_int32(c_sort(int32, A__questionmark_result!303)))) | $lesseq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)),
% 1.59/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.30 tff(84,plain,
% 1.59/1.30 ($lesseq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[83, 74])).
% 1.59/1.30 tff(85,plain,
% 1.59/1.30 ((~$greatereq(integer_of_int32(c_sort(int32, A__questionmark_result0!305)), 2)) | (~$lesseq(integer_of_int32(c_sort(int32, A__questionmark_result!303)), 1)) | (~$greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_result!303)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_x!304)))), 0)) | $lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1)),
% 1.59/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.30 tff(86,plain,
% 1.59/1.30 ($lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1)),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[85, 84, 82, 80])).
% 1.59/1.30 tff(87,plain,
% 1.59/1.30 ((-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305))))) | (~$lesseq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1)) | (~$greatereq($sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305)))), -1))),
% 1.59/1.30 inference(theory_lemma,[status(thm)],[])).
% 1.59/1.30 tff(88,plain,
% 1.59/1.30 (-1 = $sum(integer_of_int32(c_sort(int32, A__questionmark_x!304)), $product(-1, integer_of_int32(c_sort(int32, A__questionmark_result0!305))))),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[87, 86, 78])).
% 1.59/1.30 tff(89,plain,
% 1.59/1.30 ($false),
% 1.59/1.30 inference(unit_resolution,[status(thm)],[88, 63])).
% 1.59/1.30 % SZS output end Proof
%------------------------------------------------------------------------------