%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP441-1 : 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 : n014.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 01:34:07 PM UTC 2026
% Result : Unsatisfiable 8.62s 4.73s
% Output : CNFRefutation 8.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 179 ( 0 sgn 179 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = X3,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(X4,X2))))),X3)))) = X4,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = X2,
inference(superposition,[status(thm)],[c_94,c_51]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5)))) = multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X2,multiply(X6,X8)))))),
inference(superposition,[status(thm)],[c_51,c_105]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(inverse(X2),multiply(multiply(inverse(X3),multiply(multiply(inverse(X4),X5),inverse(multiply(X6,multiply(X7,X5))))),X6)),X7)),X4)),X3)))) = X2,
inference(superposition,[status(thm)],[c_105,c_94]) ).
tcf(c_1790,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))) = X3,
inference(superposition,[status(thm)],[c_125,c_105]) ).
tcf(c_1809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5))))) = X2,
inference(superposition,[status(thm)],[c_125,c_51]) ).
tcf(c_2646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,X5),inverse(multiply(inverse(X6),multiply(X0,X5)))))) = X6,
inference(superposition,[status(thm)],[c_51,c_1790]) ).
tcf(c_2661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),inverse(multiply(X3,multiply(inverse(X4),X2))))),X3))) = X4,
inference(superposition,[status(thm)],[c_51,c_1790]) ).
tcf(c_2692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(inverse(X3),multiply(X0,multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(inverse(X2),multiply(inverse(X1),X5))))))))))) = X3,
inference(superposition,[status(thm)],[c_1790,c_1790]) ).
tcf(c_2885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : multiply(X0,multiply(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3)))))),multiply(multiply(X4,multiply(multiply(inverse(X0),X5),inverse(multiply(X6,multiply(inverse(X7),X5))))),X6))) = X7,
inference(superposition,[status(thm)],[c_51,c_2661]) ).
tcf(c_4310,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(inverse(X2),X1))))) = X2,
inference(superposition,[status(thm)],[c_1790,c_2692]) ).
tcf(c_4798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),X2)))),inverse(X3)))) = X1,
inference(superposition,[status(thm)],[c_4310,c_4310]) ).
tcf(c_5642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),X3))) = X1,
inference(superposition,[status(thm)],[c_138,c_4798]) ).
tcf(c_5898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)),inverse(X2)))) = X0,
inference(superposition,[status(thm)],[c_5642,c_1790]) ).
tcf(c_5905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(X0),multiply(X0,multiply(multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)),inverse(X2)))) = X1,
inference(superposition,[status(thm)],[c_5642,c_4310]) ).
tcf(c_6528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(multiply(X1,multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X4),X3))),X2)))),multiply(X4,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_4310,c_5898]) ).
tcf(c_10304,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_6528,c_5642]) ).
tcf(c_10314,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(inverse(X1),inverse(multiply(inverse(X2),X2))))) = X0,
inference(superposition,[status(thm)],[c_6528,c_5898]) ).
tcf(c_10315,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(X0,multiply(X1,inverse(multiply(inverse(X2),X2))))) = X1,
inference(superposition,[status(thm)],[c_6528,c_5905]) ).
tcf(c_11263,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X2),X2))) = X0,
inference(superposition,[status(thm)],[c_10304,c_10314]) ).
tcf(c_12053,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[c_10304,c_11263]) ).
tcf(c_12271,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[c_11263,c_11263]) ).
tcf(c_12273,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_10315,c_12271]) ).
tcf(c_12275,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_4310,c_12273]) ).
tcf(c_13001,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(multiply(inverse(X0),multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(inverse(X4),X2))))),X3)) = multiply(inverse(X1),X4),
inference(superposition,[status(thm)],[c_2661,c_12273]) ).
tcf(c_13170,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_12273,c_12053]) ).
tcf(c_13175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),multiply(multiply(X2,X3),inverse(multiply(X4,multiply(X5,X3))))),X4)),X5))) = X2,
inference(demodulation,[status(thm)],[c_1809,c_13170]) ).
tcf(c_13177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2)))))) = inverse(X3),
inference(demodulation,[status(thm)],[c_125,c_13175]) ).
tcf(c_13188,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_2661,c_13001]) ).
tcf(c_13396,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_13170,c_10304]) ).
tcf(c_13484,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(superposition,[status(thm)],[c_12273,c_12275]) ).
tcf(c_13487,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_13170,c_12275]) ).
tcf(c_13490,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_12275,c_12273]) ).
tcf(c_13508,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c_13170,c_13484]) ).
tcf(c_13552,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[c_13396,c_13508]) ).
tcf(c_13691,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_13487,c_13188]) ).
tcf(c_13768,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(inverse(X1),X2)),multiply(inverse(X2),X1)) = X0,
inference(superposition,[status(thm)],[c_13490,c_13508]) ).
tcf(c_13815,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,multiply(inverse(X1),X2))) = multiply(multiply(inverse(X2),X1),inverse(X0)),
inference(superposition,[status(thm)],[c_13490,c_13691]) ).
tcf(c_13945,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(X1),X2))) = multiply(X0,multiply(inverse(X2),X1)),
inference(superposition,[status(thm)],[c_13768,c_13484]) ).
tcf(c_16677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(inverse(X1),multiply(multiply(X1,X2),multiply(inverse(multiply(X0,X2)),X3)))) = X3,
inference(demodulation,[status(thm)],[c_2646,c_13177,c_13945]) ).
tcf(c_16743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(inverse(X1),multiply(multiply(X1,X2),X3))) = multiply(inverse(inverse(multiply(X0,X2))),X3),
inference(superposition,[status(thm)],[c_13188,c_16677]) ).
tcf(c_16945,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,multiply(multiply(inverse(X0),X1),multiply(multiply(inverse(X1),X2),inverse(X3)))),X3) = X2,
inference(demodulation,[status(thm)],[c_2885,c_13170,c_13177,c_13815,c_16743]) ).
tcf(c_16987,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(multiply(inverse(X0),X1),inverse(X2))),X2) = X1,
inference(superposition,[status(thm)],[c_13552,c_16945]) ).
tcf(c_17164,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,inverse(X2))),X2) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12273,c_16987]) ).
tcf(c_17477,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_13484,c_17164]) ).
tcf(c_17565,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_17477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP441-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:46:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running UEQ theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 8.62/4.73 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.62/4.73 % SZS status Started for theBenchmark.p
% 8.62/4.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.62/4.73
% 8.62/4.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.62/4.73
% 8.62/4.73 % ------ iProver source info
% 8.62/4.73
% 8.62/4.73 % git: date: 2026-07-19 20:42:38 +0200
% 8.62/4.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.62/4.73 % git: non_committed_changes: false
% 8.62/4.73
% 8.62/4.73 % ------ Parsing...% successful
% 8.62/4.73
% 8.62/4.73
% 8.62/4.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.62/4.73
% 8.62/4.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.62/4.73
% 8.62/4.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.62/4.73
% 8.62/4.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.62/4.73 % ------ Proving...
% 8.62/4.73 % ------ Problem Properties
% 8.62/4.73
% 8.62/4.73 %
% 8.62/4.73 % clauses 2
% 8.62/4.73 % conjectures 1
% 8.62/4.73 % EPR 0
% 8.62/4.73 % Horn 2
% 8.62/4.73 % unary 2
% 8.62/4.73 % binary 0
% 8.62/4.73 % lits 2
% 8.62/4.73 % lits eq 2
% 8.62/4.73 % fd_pure 0
% 8.62/4.73 % fd_pseudo 0
% 8.62/4.73 % fd_cond 0
% 8.62/4.73 % fd_pseudo_cond 0
% 8.62/4.73 % AC symbols 0
% 8.62/4.73
% 8.62/4.73 % ------ Input Options Time Limit: Unbounded
% 8.62/4.73
% 8.62/4.73
% 8.62/4.73 % ------
% 8.62/4.73 % Current options:
% 8.62/4.73 % ------
% 8.62/4.73
% 8.62/4.73
% 8.62/4.73 %
% 8.62/4.73
% 8.62/4.73 % ------ Proving...
% 8.62/4.73 %
% 8.62/4.73
% 8.62/4.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.62/4.73
% 8.62/4.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.62/4.73
% 8.62/4.73
%------------------------------------------------------------------------------