%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 01:31:47 PM UTC 2026
% Result : Unsatisfiable 35.19s 12.93s
% Output : CNFRefutation 35.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 74 ( 74 unt; 6 def)
% Number of atoms : 134 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
fof(f4,axiom,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
fof(f5,axiom,
! [X0,X1] : multiply(right_division(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
fof(f7,axiom,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f8,plain,
! [X0] : identity = multiply(X0,right_inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f11,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),X1) = multiply(X0,multiply(X1,multiply(X2,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang2) ).
fof(f12,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang3) ).
tcf(c_59,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : multiply(X0,left_division(X0,X1)) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(X0,X1)) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(X0,right_inverse(X0)) = identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(X0,X1),X2),X1) = multiply(X0,multiply(X1,multiply(X2,X1))),
inference(cnf_transformation,[],[f11]) ).
tcf(c_68,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_103,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_104,definition,
iPr_def_11 = multiply(iPr_def_10,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_105,definition,
iPr_def_12 = multiply(iPr_def_11,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_106,definition,
iPr_def_13 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_107,definition,
iPr_def_14 = multiply(b,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_108,definition,
iPr_def_15 = multiply(a,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_109,negated_conjecture,
iPr_def_12 != iPr_def_15,
inference(demodulation,[status(thm)],[c_68,c_106,c_107,c_108,c_103,c_104,c_105]) ).
tcf(c_209,plain,
! [X0: $i] : left_division(X0,X0) = identity,
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_210,plain,
! [X0: $i] : left_division(X0,identity) = right_inverse(X0),
inference(superposition,[status(thm)],[c_65,c_62]) ).
tcf(c_212,plain,
left_division(a,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_103,c_62]) ).
tcf(c_213,plain,
left_division(a,iPr_def_13) = c,
inference(superposition,[status(thm)],[c_106,c_62]) ).
tcf(c_214,plain,
left_division(iPr_def_10,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_104,c_62]) ).
tcf(c_215,plain,
left_division(iPr_def_11,iPr_def_12) = c,
inference(superposition,[status(thm)],[c_105,c_62]) ).
tcf(c_216,plain,
left_division(b,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_107,c_62]) ).
tcf(c_222,plain,
multiply(a,b) = iPr_def_10,
inference(superposition,[status(thm)],[c_212,c_61]) ).
tcf(c_232,plain,
multiply(a,c) = iPr_def_13,
inference(superposition,[status(thm)],[c_213,c_61]) ).
tcf(c_234,plain,
multiply(iPr_def_10,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_214,c_61]) ).
tcf(c_236,plain,
multiply(iPr_def_11,c) = iPr_def_12,
inference(superposition,[status(thm)],[c_215,c_61]) ).
tcf(c_238,plain,
multiply(b,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_216,c_61]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,multiply(X1,X0))) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_59,c_67]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(right_division(X0,X1),multiply(X1,multiply(X2,X1))) = multiply(multiply(X0,X2),X1),
inference(superposition,[status(thm)],[c_63,c_67]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),multiply(X1,right_inverse(X0)))) = multiply(multiply(identity,X1),right_inverse(X0)),
inference(superposition,[status(thm)],[c_65,c_67]) ).
tcf(c_372,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(a,multiply(X0,a))) = multiply(multiply(iPr_def_11,X0),a),
inference(superposition,[status(thm)],[c_234,c_67]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_361,c_59]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),multiply(X1,right_inverse(X0)))) = multiply(X1,right_inverse(X0)),
inference(demodulation,[status(thm)],[c_365,c_59]) ).
tcf(c_547,plain,
! [X0: $i] : multiply(X0,multiply(right_inverse(X0),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_65,c_385]) ).
tcf(c_552,plain,
multiply(a,multiply(c,a)) = multiply(iPr_def_13,a),
inference(superposition,[status(thm)],[c_232,c_385]) ).
tcf(c_570,plain,
! [X0: $i] : multiply(X0,multiply(right_inverse(X0),X0)) = X0,
inference(demodulation,[status(thm)],[c_547,c_59]) ).
tcf(c_617,plain,
! [X0: $i] : multiply(right_inverse(X0),X0) = left_division(X0,X0),
inference(superposition,[status(thm)],[c_570,c_62]) ).
tcf(c_621,plain,
! [X0: $i] : multiply(right_inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_617,c_209]) ).
tcf(c_654,plain,
! [X0: $i] : left_division(right_inverse(X0),identity) = X0,
inference(superposition,[status(thm)],[c_621,c_62]) ).
tcf(c_655,plain,
! [X0: $i] : right_inverse(right_inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_654,c_210]) ).
tcf(c_1076,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,right_inverse(X1)),multiply(right_inverse(X1),identity)) = multiply(multiply(X0,X1),right_inverse(X1)),
inference(superposition,[status(thm)],[c_65,c_364]) ).
tcf(c_1093,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,X1),multiply(X1,identity)) = multiply(multiply(X0,right_inverse(X1)),X1),
inference(superposition,[status(thm)],[c_621,c_364]) ).
tcf(c_1106,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,right_inverse(X1)),X1) = X0,
inference(demodulation,[status(thm)],[c_1093,c_60,c_63]) ).
tcf(c_1108,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),right_inverse(X1)) = X0,
inference(demodulation,[status(thm)],[c_1076,c_60,c_63]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i] : right_division(X0,right_inverse(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_63,c_1106]) ).
tcf(c_1235,plain,
multiply(iPr_def_10,right_inverse(b)) = a,
inference(superposition,[status(thm)],[c_222,c_1108]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(right_division(X0,right_inverse(X1)),multiply(right_inverse(X1),X2)) = multiply(multiply(X0,multiply(X2,X1)),right_inverse(X1)),
inference(superposition,[status(thm)],[c_1108,c_364]) ).
tcf(c_1272,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X2)),right_inverse(X2)) = multiply(multiply(X0,X2),multiply(right_inverse(X2),X1)),
inference(light_normalisation,[status(thm)],[c_1267,c_1149]) ).
tcf(c_1286,plain,
left_division(iPr_def_10,a) = right_inverse(b),
inference(superposition,[status(thm)],[c_1235,c_62]) ).
tcf(c_1751,plain,
multiply(multiply(iPr_def_11,c),a) = multiply(iPr_def_10,multiply(iPr_def_13,a)),
inference(superposition,[status(thm)],[c_552,c_372]) ).
tcf(c_1767,plain,
multiply(iPr_def_10,multiply(iPr_def_13,a)) = multiply(iPr_def_12,a),
inference(light_normalisation,[status(thm)],[c_1751,c_236]) ).
tcf(c_7026,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_1108,c_389]) ).
tcf(c_7154,plain,
! [X0: $i,X1: $i] : left_division(right_inverse(X0),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_61,c_7026]) ).
tcf(c_7160,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_655,c_7026]) ).
tcf(c_7174,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),X1) = left_division(X0,X1),
inference(superposition,[status(thm)],[c_7026,c_62]) ).
tcf(c_8239,plain,
multiply(right_inverse(iPr_def_10),multiply(iPr_def_12,a)) = multiply(iPr_def_13,a),
inference(superposition,[status(thm)],[c_1767,c_7160]) ).
tcf(c_147590,plain,
multiply(multiply(right_inverse(iPr_def_10),a),multiply(right_inverse(a),iPr_def_12)) = multiply(multiply(iPr_def_13,a),right_inverse(a)),
inference(superposition,[status(thm)],[c_8239,c_1272]) ).
tcf(c_147604,plain,
multiply(left_division(iPr_def_10,a),left_division(a,iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_147590,c_1108,c_7174]) ).
tcf(c_147605,plain,
multiply(right_inverse(b),left_division(a,iPr_def_12)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_147604,c_1286]) ).
tcf(c_147916,plain,
left_division(right_inverse(b),iPr_def_13) = left_division(a,iPr_def_12),
inference(superposition,[status(thm)],[c_147605,c_62]) ).
tcf(c_147942,plain,
multiply(b,iPr_def_13) = left_division(a,iPr_def_12),
inference(demodulation,[status(thm)],[c_147916,c_7154]) ).
tcf(c_147943,plain,
left_division(a,iPr_def_12) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_147942,c_238]) ).
tcf(c_148182,plain,
multiply(a,iPr_def_14) = iPr_def_12,
inference(superposition,[status(thm)],[c_147943,c_61]) ).
tcf(c_148222,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_108,c_148182]) ).
tcf(c_148223,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_148222,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.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 14:07:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.42 Running UEQ theorem proving
% 0.13/0.42 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 35.19/12.93 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 35.19/12.93 % SZS status Started for theBenchmark.p
% 35.19/12.93 % SZS status Unsatisfiable for theBenchmark.p
% 35.19/12.93
% 35.19/12.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.19/12.93
% 35.19/12.93 % ------ iProver source info
% 35.19/12.93
% 35.19/12.93 % git: date: 2026-07-19 20:42:38 +0200
% 35.19/12.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.19/12.93 % git: non_committed_changes: false
% 35.19/12.93
% 35.19/12.93 % ------ Parsing...% successful
% 35.19/12.93
% 35.19/12.93
% 35.19/12.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.19/12.93
% 35.19/12.93 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 35.19/12.93
% 35.19/12.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.19/12.93
% 35.19/12.93 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 35.19/12.93 % ------ Proving...
% 35.19/12.93 % ------ Problem Properties
% 35.19/12.93
% 35.19/12.93 %
% 35.19/12.93 % clauses 16
% 35.19/12.93 % conjectures 1
% 35.19/12.93 % EPR 1
% 35.19/12.93 % Horn 16
% 35.19/12.93 % unary 16
% 35.19/12.93 % binary 0
% 35.19/12.93 % lits 16
% 35.19/12.93 % lits eq 16
% 35.19/12.93 % fd_pure 0
% 35.19/12.93 % fd_pseudo 0
% 35.19/12.93 % fd_cond 0
% 35.19/12.93 % fd_pseudo_cond 0
% 35.19/12.93 % AC symbols 0
% 35.19/12.93
% 35.19/12.93 % ------ Input Options Time Limit: Unbounded
% 35.19/12.93
% 35.19/12.93
% 35.19/12.93 % ------
% 35.19/12.93 % Current options:
% 35.19/12.93 % ------
% 35.19/12.93
% 35.19/12.93
% 35.19/12.93 %
% 35.19/12.93
% 35.19/12.93 % ------ Proving...
% 35.19/12.93 %
% 35.19/12.93
% 35.19/12.93 % SZS status Unsatisfiable for theBenchmark.p
% 35.19/12.93
% 35.19/12.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.19/12.94
% 35.19/12.94
%------------------------------------------------------------------------------