%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:51 PM UTC 2026
% Result : Unsatisfiable 7.28s 1.78s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 137 ( 37 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 126 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)),inverse(multiply(X3,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)))))))))),multiply(X0,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4))))) = X1,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_60]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)))) = X1,
inference(demodulation,[status(thm)],[c_61,c_63]) ).
tcf(c_65,plain,
! [X0: $i] : iPr_def_10(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_51,c_62]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1)) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_63,c_63]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1))) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_85,plain,
! [X0: $i] : inverse(iPr_def_10(X0)) = iPr_def_10(inverse(X0)),
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_96,plain,
! [X0: $i] : inverse(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_85,c_65]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,iPr_def_10(X2)),inverse(multiply(inverse(multiply(X0,iPr_def_10(X2))),multiply(X0,iPr_def_10(X2)))))))))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_95,c_79]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_65,c_82]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1)) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_65,c_84]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_84,c_65]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3))))))))) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X4)))),X5),
inference(superposition,[status(thm)],[c_165,c_165]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),iPr_def_10(X4))),X5)),
inference(superposition,[status(thm)],[c_188,c_188]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(iPr_def_10(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3))))))))))) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X4)))),iPr_def_10(X5)),
inference(superposition,[status(thm)],[c_165,c_195]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,iPr_def_10(X2)),inverse(multiply(inverse(multiply(X0,iPr_def_10(X2))),multiply(X0,iPr_def_10(X2)))))))))),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_96,c_141]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),iPr_def_10(X4))),X5)),
inference(demodulation,[status(thm)],[c_427,c_65]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))) = iPr_def_11(X1,X2,X4),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_634]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),X1) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_384,c_636]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),X1) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_639,c_96]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(inverse(iPr_def_11(X0,X2,inverse(X3))))),
inference(demodulation,[status(thm)],[c_442,c_636]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),iPr_def_10(X1)) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_652,c_65,c_96]) ).
tcf(c_1974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),inverse(iPr_def_10(iPr_def_10(X1))))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(inverse(X3))))),X3),
inference(superposition,[status(thm)],[c_470,c_640]) ).
tcf(c_1976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),inverse(iPr_def_10(iPr_def_10(X1))))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(X3)))),iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_470,c_653]) ).
tcf(c_1987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),iPr_def_10(X1))) = multiply(X3,iPr_def_10(X3)),
inference(demodulation,[status(thm)],[c_1976,c_65,c_96]) ).
tcf(c_1988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),iPr_def_10(X1))) = multiply(inverse(X3),X3),
inference(demodulation,[status(thm)],[c_1974,c_65,c_96]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(X1,iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1988,c_1987]) ).
tcf(c_3108,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_12,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_3061]) ).
tcf(c_3536,plain,
multiply(inverse(b1),b1) != iPr_def_12,
inference(demodulation,[status(thm)],[c_52,c_3108]) ).
tcf(c_3540,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3536,c_3108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP418-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:45:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running UEQ theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 7.28/1.78 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 7.28/1.78 % SZS status Started for theBenchmark.p
% 7.28/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 7.28/1.78
% 7.28/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.28/1.78
% 7.28/1.78 % ------ iProver source info
% 7.28/1.78
% 7.28/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 7.28/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.28/1.78 % git: non_committed_changes: false
% 7.28/1.78
% 7.28/1.78 % ------ Parsing...% successful
% 7.28/1.78
% 7.28/1.78
% 7.28/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.28/1.78 % ------ Proving...
% 7.28/1.78 % ------ Problem Properties
% 7.28/1.78
% 7.28/1.78 %
% 7.28/1.78 % clauses 2
% 7.28/1.78 % conjectures 1
% 7.28/1.78 % EPR 0
% 7.28/1.78 % Horn 2
% 7.28/1.78 % unary 2
% 7.28/1.78 % binary 0
% 7.28/1.78 % lits 2
% 7.28/1.78 % lits eq 2
% 7.28/1.78 % fd_pure 0
% 7.28/1.78 % fd_pseudo 0
% 7.28/1.78 % fd_cond 0
% 7.28/1.78 % fd_pseudo_cond 0
% 7.28/1.78 % AC symbols 0
% 7.28/1.78
% 7.28/1.78 % ------ Input Options Time Limit: Unbounded
% 7.28/1.78
% 7.28/1.78
% 7.28/1.78 % ------
% 7.28/1.78 % Current options:
% 7.28/1.78 % ------
% 7.28/1.78
% 7.28/1.78
% 7.28/1.78 %
% 7.28/1.78
% 7.28/1.78 % ------ Proving...
% 7.28/1.78 %
% 7.28/1.78
% 7.28/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 7.28/1.78
% 7.28/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.28/1.78
% 7.28/1.78
%------------------------------------------------------------------------------