%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 12.52s 2.74s
% Output : CNFRefutation 12.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 160 ( 0 sgn 160 !; 0 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[],[f3]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X0))),X3))),X0)) = multiply(X1,inverse(multiply(multiply(multiply(inverse(X2),X2),inverse(X3)),X2))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1)))) = X2,
inference(superposition,[status(thm)],[c_94,c_51]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),inverse(X0))),multiply(inverse(multiply(X1,inverse(X2))),X3)))),X0)) = X3,
inference(superposition,[status(thm)],[c_94,c_51]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(multiply(inverse(X1),X1),inverse(X0))),X2))),X0) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(X2,X1)))),
inference(superposition,[status(thm)],[c_51,c_120]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,X2)))),X0)) = X2,
inference(superposition,[status(thm)],[c_131,c_131]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_362,c_120]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(superposition,[status(thm)],[c_362,c_394]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X0)))),X3)) = multiply(inverse(multiply(X4,X1)),multiply(X4,X3)),
inference(superposition,[status(thm)],[c_362,c_489]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(multiply(multiply(multiply(inverse(multiply(X3,X2)),multiply(X3,X2)),inverse(X4)),multiply(X1,X2))))) = X4,
inference(superposition,[status(thm)],[c_489,c_120]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(multiply(multiply(inverse(multiply(X1,X2)),multiply(X1,X2)),inverse(multiply(inverse(multiply(X0,inverse(multiply(X3,X2)))),X4))),multiply(X3,X2)))) = X4,
inference(superposition,[status(thm)],[c_489,c_51]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),inverse(multiply(inverse(multiply(X2,inverse(multiply(X3,X1)))),multiply(X2,X4)))),multiply(X3,X1))) = X4,
inference(superposition,[status(thm)],[c_489,c_362]) ).
tcf(c_4826,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(multiply(X2,X0)))))) = X2,
inference(superposition,[status(thm)],[c_236,c_648]) ).
tcf(c_4828,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),X2),X1))))) = X2,
inference(superposition,[status(thm)],[c_236,c_652]) ).
tcf(c_4842,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(multiply(inverse(X1),X1),inverse(X0))),multiply(multiply(inverse(X1),X1),inverse(X2))))),X0) = X2,
inference(superposition,[status(thm)],[c_236,c_120]) ).
tcf(c_5919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),inverse(X2)) = multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,X1)),inverse(X2)),
inference(superposition,[status(thm)],[c_647,c_4826]) ).
tcf(c_7199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),X2) = multiply(multiply(inverse(multiply(X3,X1)),multiply(X3,X1)),X2),
inference(superposition,[status(thm)],[c_4828,c_5919]) ).
tcf(c_8188,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(multiply(X1,inverse(X0))),multiply(X1,inverse(X2))))),X0) = X2,
inference(superposition,[status(thm)],[c_489,c_4842]) ).
tcf(c_8483,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)),X2) = multiply(multiply(inverse(X3),X3),X2),
inference(superposition,[status(thm)],[c_8188,c_7199]) ).
tcf(c_8503,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X1)) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_8188,c_620]) ).
tcf(c_8863,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_8503,c_8503]) ).
tcf(c_9167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X2),X2),X3),X1))))) = X3,
inference(superposition,[status(thm)],[c_8863,c_4828]) ).
tcf(c_9177,plain,
! [X0: $i] : multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[c_8863,c_52]) ).
tcf(c_9285,plain,
! [X0: $i,X1: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X1),X1))),X0) = X0,
inference(superposition,[status(thm)],[c_8863,c_8188]) ).
tcf(c_9830,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X1),X1))),X2) = X2,
inference(superposition,[status(thm)],[c_8863,c_9285]) ).
tcf(c_9947,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X1),X1))),X2)),X3) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(superposition,[status(thm)],[c_9830,c_489]) ).
tcf(c_9966,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(X1),X2),
inference(light_normalisation,[status(thm)],[c_9947,c_9830]) ).
tcf(c_10012,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X1),X2)) = multiply(inverse(X1),X2),
inference(superposition,[status(thm)],[c_8863,c_9966]) ).
tcf(c_10027,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),X3)) = multiply(inverse(X2),multiply(X0,X3)),
inference(superposition,[status(thm)],[c_9966,c_9966]) ).
tcf(c_10346,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(X0),X0),X1) = multiply(multiply(inverse(X2),X2),X1),
inference(demodulation,[status(thm)],[c_8483,c_9966]) ).
tcf(c_11002,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(inverse(X0)),inverse(multiply(multiply(multiply(inverse(X1),X1),X2),X0)))) = X2,
inference(demodulation,[status(thm)],[c_9167,c_9966]) ).
tcf(c_11023,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X0)),multiply(X1,X2)) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_11002,c_10012]) ).
tcf(c_11037,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(inverse(inverse(X1)),inverse(multiply(multiply(multiply(inverse(X2),X2),X0),X1)))),a2) != a2,
inference(superposition,[status(thm)],[c_11002,c_9177]) ).
tcf(c_11219,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[c_9830,c_11023]) ).
tcf(c_11478,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,multiply(inverse(X1),X1))),X2)),X3) = multiply(inverse(X2),multiply(X0,X3)),
inference(superposition,[status(thm)],[c_11219,c_10027]) ).
tcf(c_12382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(X1,multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),X3))) = multiply(inverse(X0),X3),
inference(superposition,[status(thm)],[c_11478,c_9966]) ).
tcf(c_14263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(X1,multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),X3))) = multiply(X0,X3),
inference(superposition,[status(thm)],[c_11002,c_12382]) ).
tcf(c_14596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X1),X1))),X2) = multiply(X3,multiply(inverse(multiply(X3,multiply(inverse(X4),X4))),X2)),
inference(superposition,[status(thm)],[c_14263,c_9830]) ).
tcf(c_14626,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(X0,multiply(inverse(X1),X1))),X2)) = X2,
inference(light_normalisation,[status(thm)],[c_14596,c_9830]) ).
tcf(c_14882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))),X2),multiply(inverse(inverse(X3)),inverse(multiply(X2,X3)))),a2) != a2,
inference(superposition,[status(thm)],[c_14626,c_11037]) ).
tcf(c_14903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2))),X3)) = X3,
inference(superposition,[status(thm)],[c_14626,c_10346]) ).
tcf(c_15407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))),inverse(X2)),multiply(inverse(inverse(X2)),inverse(multiply(inverse(X3),X3)))),a2) != a2,
inference(superposition,[status(thm)],[c_8863,c_14882]) ).
tcf(c_16472,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(inverse(multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))),X2),multiply(inverse(X2),inverse(multiply(inverse(X3),X3)))),a2) != a2,
inference(superposition,[status(thm)],[c_11002,c_15407]) ).
tcf(c_16498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2))),inverse(multiply(inverse(X3),X3)))),a2) != a2,
inference(superposition,[status(thm)],[c_10346,c_16472]) ).
tcf(c_16589,plain,
$false,
inference(ground_joinability,[status(thm)],[c_16498,c_11219,c_14903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP413-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 14:42:39 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running UEQ theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 12.52/2.74 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 12.52/2.74 % SZS status Started for theBenchmark.p
% 12.52/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 12.52/2.74
% 12.52/2.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.52/2.74
% 12.52/2.74 % ------ iProver source info
% 12.52/2.74
% 12.52/2.74 % git: date: 2026-07-19 20:42:38 +0200
% 12.52/2.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.52/2.74 % git: non_committed_changes: false
% 12.52/2.74
% 12.52/2.74 % ------ Parsing...% successful
% 12.52/2.74
% 12.52/2.74
% 12.52/2.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.52/2.74
% 12.52/2.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 12.52/2.74
% 12.52/2.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.52/2.74
% 12.52/2.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 12.52/2.74 % ------ Proving...
% 12.52/2.74 % ------ Problem Properties
% 12.52/2.74
% 12.52/2.74 %
% 12.52/2.74 % clauses 2
% 12.52/2.74 % conjectures 1
% 12.52/2.74 % EPR 0
% 12.52/2.74 % Horn 2
% 12.52/2.74 % unary 2
% 12.52/2.74 % binary 0
% 12.52/2.74 % lits 2
% 12.52/2.74 % lits eq 2
% 12.52/2.74 % fd_pure 0
% 12.52/2.74 % fd_pseudo 0
% 12.52/2.74 % fd_cond 0
% 12.52/2.74 % fd_pseudo_cond 0
% 12.52/2.74 % AC symbols 0
% 12.52/2.74
% 12.52/2.74 % ------ Input Options Time Limit: Unbounded
% 12.52/2.74
% 12.52/2.74
% 12.52/2.74 % ------
% 12.52/2.74 % Current options:
% 12.52/2.74 % ------
% 12.52/2.74
% 12.52/2.74
% 12.52/2.74 %
% 12.52/2.74
% 12.52/2.74 % ------ Proving...
% 12.52/2.74 %
% 12.52/2.74
% 12.52/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 12.52/2.74
% 12.52/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.52/2.74
% 12.52/2.74
%------------------------------------------------------------------------------