%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 01:33:39 PM UTC 2026
% Result : Unsatisfiable 34.63s 7.78s
% Output : CNFRefutation 34.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 47 unt; 4 def)
% Number of atoms : 167 ( 58 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 20 ( 14 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X1 = X2
| multiply(X0,X1) != multiply(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
fof(f4,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X0,commutator(X0,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(commutator(X0,X1),X2) = multiply(X2,commutator(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nilpotency) ).
fof(f6,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator_is_associative) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( multiply(X0,X1) != multiply(X0,X2) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,commutator(X1,X0))) = multiply(X1,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(commutator(X0,X1),X2) = multiply(X2,commutator(X0,X1)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_91,definition,
iPr_def_10 = commutator(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_92,definition,
iPr_def_11 = commutator(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_93,definition,
iPr_def_12 = commutator(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_94,definition,
iPr_def_13 = commutator(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_95,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_60,c_93,c_94,c_91,c_92]) ).
tcf(c_154,plain,
multiply(c,multiply(iPr_def_10,iPr_def_11)) = multiply(iPr_def_10,c),
inference(superposition,[status(thm)],[c_92,c_58]) ).
tcf(c_192,plain,
! [X0: $i] : multiply(X0,iPr_def_10) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_91,c_59]) ).
tcf(c_193,plain,
! [X0: $i] : multiply(X0,iPr_def_12) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_93,c_59]) ).
tcf(c_194,plain,
! [X0: $i] : multiply(X0,iPr_def_11) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_92,c_59]) ).
tcf(c_195,plain,
! [X0: $i] : multiply(X0,iPr_def_13) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_94,c_59]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_10)) = multiply(iPr_def_10,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_192,c_55]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] : multiply(multiply(iPr_def_12,X0),X1) = multiply(X0,multiply(iPr_def_12,X1)),
inference(superposition,[status(thm)],[c_193,c_55]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_12 )
| ( multiply(X0,X1) != multiply(iPr_def_12,X0) ) ),
inference(superposition,[status(thm)],[c_193,c_57]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_12)) = multiply(iPr_def_12,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_55]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] : multiply(multiply(iPr_def_11,X0),X1) = multiply(X0,multiply(iPr_def_11,X1)),
inference(superposition,[status(thm)],[c_194,c_55]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_11 )
| ( multiply(X0,X1) != multiply(iPr_def_11,X0) ) ),
inference(superposition,[status(thm)],[c_194,c_57]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_11)) = multiply(iPr_def_11,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_194,c_55]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] : multiply(multiply(iPr_def_13,X0),X1) = multiply(X0,multiply(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_195,c_55]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_13)) = multiply(iPr_def_13,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_195,c_55]) ).
tcf(c_488,plain,
multiply(iPr_def_10,multiply(iPr_def_11,c)) = multiply(iPr_def_10,c),
inference(demodulation,[status(thm)],[c_154,c_302,c_378]) ).
tcf(c_491,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(multiply(iPr_def_11,c),X0)) = multiply(multiply(iPr_def_10,c),X0),
inference(superposition,[status(thm)],[c_488,c_55]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_12,X1)) = multiply(iPr_def_12,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_339,c_55]) ).
tcf(c_860,plain,
multiply(iPr_def_10,multiply(iPr_def_12,multiply(iPr_def_11,c))) = multiply(iPr_def_12,multiply(iPr_def_10,c)),
inference(superposition,[status(thm)],[c_488,c_827]) ).
tcf(c_880,plain,
! [X0: $i] : multiply(X0,multiply(iPr_def_12,commutator(X0,iPr_def_12))) = multiply(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_827,c_58]) ).
tcf(c_1263,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_12)) = multiply(X0,multiply(iPr_def_12,X1)),
inference(superposition,[status(thm)],[c_342,c_827]) ).
tcf(c_1472,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_11,X1)) = multiply(iPr_def_11,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_375,c_55]) ).
tcf(c_1507,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_11,multiply(iPr_def_12,X1))) = multiply(iPr_def_11,multiply(iPr_def_12,multiply(X0,X1))),
inference(superposition,[status(thm)],[c_827,c_1472]) ).
tcf(c_1923,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_13,X1)) = multiply(iPr_def_13,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_411,c_55]) ).
tcf(c_2325,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_13)) = multiply(X0,multiply(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_414,c_1923]) ).
tcf(c_5239,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,iPr_def_12))) = multiply(X0,multiply(iPr_def_12,multiply(X1,X2))),
inference(superposition,[status(thm)],[c_55,c_1263]) ).
tcf(c_10011,plain,
! [X0: $i] :
( ( multiply(iPr_def_12,commutator(X0,iPr_def_12)) = iPr_def_12 )
| ( multiply(X0,iPr_def_12) != multiply(iPr_def_12,X0) ) ),
inference(superposition,[status(thm)],[c_880,c_341]) ).
tcf(c_10085,plain,
! [X0: $i] : multiply(iPr_def_12,commutator(X0,iPr_def_12)) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_10011,c_193]) ).
tcf(c_11381,plain,
! [X0: $i] :
( ( iPr_def_11 = iPr_def_13 )
| ( multiply(iPr_def_11,X0) != multiply(iPr_def_13,X0) ) ),
inference(superposition,[status(thm)],[c_195,c_377]) ).
tcf(c_11453,plain,
! [X0: $i] : multiply(iPr_def_11,X0) != multiply(iPr_def_13,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_11381,c_95]) ).
tcf(c_12417,plain,
multiply(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_94,c_10085]) ).
tcf(c_12595,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_13,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_12417,c_55]) ).
tcf(c_13295,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,iPr_def_13)) != multiply(iPr_def_11,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_414,c_11453]) ).
tcf(c_14631,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(X1,iPr_def_12),iPr_def_13)) != multiply(iPr_def_11,multiply(iPr_def_12,multiply(X0,X1))),
inference(superposition,[status(thm)],[c_342,c_13295]) ).
tcf(c_41910,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,multiply(c,X0))) = multiply(iPr_def_10,multiply(c,X0)),
inference(demodulation,[status(thm)],[c_491,c_55]) ).
tcf(c_41931,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,multiply(X0,c))) = multiply(iPr_def_10,multiply(X0,c)),
inference(superposition,[status(thm)],[c_58,c_41910]) ).
tcf(c_59600,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11,multiply(iPr_def_12,multiply(X0,X1))) != multiply(X0,multiply(iPr_def_12,X1)),
inference(demodulation,[status(thm)],[c_14631,c_2325,c_5239,c_12595]) ).
tcf(c_59687,plain,
multiply(iPr_def_10,multiply(iPr_def_12,multiply(iPr_def_11,c))) != multiply(iPr_def_11,multiply(iPr_def_12,multiply(iPr_def_10,c))),
inference(superposition,[status(thm)],[c_488,c_59600]) ).
tcf(c_59747,plain,
$false,
inference(ground_joinability,[status(thm)],[c_59687,c_827,c_860,c_1507,c_41931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n001.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 14:46:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 34.63/7.78 % SZS status Started for theBenchmark.p
% 34.63/7.78 % SZS status Unsatisfiable for theBenchmark.p
% 34.63/7.78
% 34.63/7.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.63/7.78
% 34.63/7.78 % ------ iProver source info
% 34.63/7.78
% 34.63/7.78 % git: date: 2026-07-19 20:42:38 +0200
% 34.63/7.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.63/7.78 % git: non_committed_changes: false
% 34.63/7.78
% 34.63/7.78 % ------ Parsing...% successful
% 34.63/7.78
% 34.63/7.78
% 34.63/7.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.63/7.78
% 34.63/7.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.63/7.78
% 34.63/7.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.63/7.78
% 34.63/7.78 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 34.63/7.78 % ------ Proving...
% 34.63/7.78 % ------ Problem Properties
% 34.63/7.78
% 34.63/7.78 %
% 34.63/7.78 % clauses 10
% 34.63/7.78 % conjectures 1
% 34.63/7.78 % EPR 1
% 34.63/7.78 % Horn 10
% 34.63/7.78 % unary 8
% 34.63/7.78 % binary 2
% 34.63/7.78 % lits 12
% 34.63/7.78 % lits eq 12
% 34.63/7.78 % fd_pure 0
% 34.63/7.78 % fd_pseudo 0
% 34.63/7.78 % fd_cond 0
% 34.63/7.78 % fd_pseudo_cond 2
% 34.63/7.78 % AC symbols 0
% 34.63/7.78
% 34.63/7.78 % ------ Schedule dynamic 5 is on
% 34.63/7.78
% 34.63/7.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.63/7.78
% 34.63/7.78
% 34.63/7.78 % ------
% 34.63/7.78 % Current options:
% 34.63/7.78 % ------
% 34.63/7.78
% 34.63/7.78
% 34.63/7.78 %
% 34.63/7.78
% 34.63/7.78 % ------ Proving...
% 34.63/7.78 %
% 34.63/7.78
% 34.63/7.78 % SZS status Unsatisfiable for theBenchmark.p
% 34.63/7.78
% 34.63/7.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.63/7.78
% 34.63/7.78
%------------------------------------------------------------------------------