%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:31:47 PM UTC 2026
% Result : Unsatisfiable 8.49s 11.83s
% Output : CNFRefutation 8.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 76 unt; 6 def)
% Number of atoms : 143 ( 75 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 : 7 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,left_division(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_left_division) ).
fof(f4,axiom,
! [X0,X1] : left_division(X0,multiply(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_division_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,right_inverse(X0)) = identity,
file('/export/starexec/sandbox2/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),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang3) ).
fof(f12,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang1) ).
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_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),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(cnf_transformation,[],[f11]) ).
tcf(c_68,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_103,definition,
iPr_def_10 = multiply(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_104,definition,
iPr_def_11 = multiply(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_105,definition,
iPr_def_12 = multiply(iPr_def_11,a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_106,definition,
iPr_def_13 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_107,definition,
iPr_def_14 = multiply(c,a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_108,definition,
iPr_def_15 = multiply(iPr_def_13,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_107,c_106,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(b,iPr_def_10) = c,
inference(superposition,[status(thm)],[c_103,c_62]) ).
tcf(c_213,plain,
left_division(a,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_106,c_62]) ).
tcf(c_214,plain,
left_division(c,iPr_def_14) = a,
inference(superposition,[status(thm)],[c_107,c_62]) ).
tcf(c_215,plain,
left_division(a,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_104,c_62]) ).
tcf(c_216,plain,
left_division(iPr_def_11,iPr_def_12) = a,
inference(superposition,[status(thm)],[c_105,c_62]) ).
tcf(c_222,plain,
multiply(b,c) = iPr_def_10,
inference(superposition,[status(thm)],[c_212,c_61]) ).
tcf(c_232,plain,
multiply(a,b) = iPr_def_13,
inference(superposition,[status(thm)],[c_213,c_61]) ).
tcf(c_234,plain,
multiply(c,a) = iPr_def_14,
inference(superposition,[status(thm)],[c_214,c_61]) ).
tcf(c_236,plain,
multiply(a,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_215,c_61]) ).
tcf(c_238,plain,
multiply(iPr_def_11,a) = iPr_def_12,
inference(superposition,[status(thm)],[c_216,c_61]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(left_division(X0,X1),multiply(X0,X2))) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[c_61,c_67]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,identity))) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_67,c_60]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X0,left_division(multiply(multiply(X0,X1),X0),X2)))) = X2,
inference(superposition,[status(thm)],[c_67,c_61]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_387,c_60]) ).
tcf(c_554,plain,
! [X0: $i] : multiply(X0,multiply(right_inverse(X0),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_65,c_394]) ).
tcf(c_574,plain,
! [X0: $i] : multiply(X0,multiply(right_inverse(X0),X0)) = X0,
inference(demodulation,[status(thm)],[c_554,c_59]) ).
tcf(c_612,plain,
! [X0: $i] : multiply(right_inverse(X0),X0) = left_division(X0,X0),
inference(superposition,[status(thm)],[c_574,c_62]) ).
tcf(c_615,plain,
! [X0: $i] : multiply(right_inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_612,c_209]) ).
tcf(c_643,plain,
! [X0: $i] : left_division(right_inverse(X0),identity) = X0,
inference(superposition,[status(thm)],[c_615,c_62]) ).
tcf(c_644,plain,
! [X0: $i] : right_inverse(right_inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_643,c_210]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_division(X0,X1),identity)) = multiply(multiply(X1,X0),right_inverse(X0)),
inference(superposition,[status(thm)],[c_65,c_370]) ).
tcf(c_736,plain,
! [X0: $i] : multiply(a,multiply(left_division(a,X0),iPr_def_13)) = multiply(multiply(X0,a),b),
inference(superposition,[status(thm)],[c_232,c_370]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),right_inverse(X1)) = X0,
inference(demodulation,[status(thm)],[c_732,c_60,c_61]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i] : multiply(X0,right_inverse(left_division(X1,X0))) = X1,
inference(superposition,[status(thm)],[c_61,c_757]) ).
tcf(c_833,plain,
multiply(iPr_def_10,right_inverse(c)) = b,
inference(superposition,[status(thm)],[c_222,c_757]) ).
tcf(c_839,plain,
multiply(iPr_def_11,right_inverse(iPr_def_10)) = a,
inference(superposition,[status(thm)],[c_236,c_757]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] : left_division(multiply(X0,X1),X0) = right_inverse(X1),
inference(superposition,[status(thm)],[c_757,c_62]) ).
tcf(c_989,plain,
left_division(iPr_def_11,a) = right_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_839,c_62]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] : right_inverse(left_division(X0,X1)) = left_division(X1,X0),
inference(superposition,[status(thm)],[c_829,c_62]) ).
tcf(c_1523,plain,
! [X0: $i,X1: $i] : multiply(left_division(X0,X1),left_division(X1,X0)) = identity,
inference(superposition,[status(thm)],[c_1221,c_615]) ).
tcf(c_1923,plain,
multiply(iPr_def_10,left_division(iPr_def_11,a)) = identity,
inference(superposition,[status(thm)],[c_215,c_1523]) ).
tcf(c_1969,plain,
multiply(iPr_def_10,right_inverse(iPr_def_10)) = identity,
inference(light_normalisation,[status(thm)],[c_1923,c_989]) ).
tcf(c_2953,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X0,left_division(multiply(X0,multiply(X1,X0)),X2)))) = X2,
inference(light_normalisation,[status(thm)],[c_388,c_394]) ).
tcf(c_3001,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),multiply(X0,left_division(multiply(X0,identity),X1)))) = X1,
inference(superposition,[status(thm)],[c_615,c_2953]) ).
tcf(c_3017,plain,
! [X0: $i] : multiply(right_inverse(iPr_def_10),multiply(iPr_def_10,multiply(right_inverse(iPr_def_10),left_division(multiply(right_inverse(iPr_def_10),identity),X0)))) = X0,
inference(superposition,[status(thm)],[c_1969,c_2953]) ).
tcf(c_3060,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(right_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_3001,c_60,c_61]) ).
tcf(c_3063,plain,
! [X0: $i] : multiply(right_inverse(iPr_def_10),multiply(iPr_def_10,X0)) = X0,
inference(demodulation,[status(thm)],[c_3017,c_60,c_61]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i] : left_division(right_inverse(X0),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_61,c_3060]) ).
tcf(c_3439,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_644,c_3060]) ).
tcf(c_3446,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),X1) = left_division(X0,X1),
inference(superposition,[status(thm)],[c_3060,c_62]) ).
tcf(c_3635,plain,
multiply(right_inverse(iPr_def_10),b) = right_inverse(c),
inference(superposition,[status(thm)],[c_833,c_3063]) ).
tcf(c_5653,plain,
multiply(right_inverse(iPr_def_11),iPr_def_12) = a,
inference(superposition,[status(thm)],[c_238,c_3439]) ).
tcf(c_5738,plain,
left_division(a,right_inverse(iPr_def_11)) = right_inverse(iPr_def_12),
inference(superposition,[status(thm)],[c_5653,c_854]) ).
tcf(c_16311,plain,
multiply(multiply(right_inverse(iPr_def_11),a),b) = multiply(a,multiply(right_inverse(iPr_def_12),iPr_def_13)),
inference(superposition,[status(thm)],[c_5738,c_736]) ).
tcf(c_16341,plain,
multiply(left_division(iPr_def_11,a),b) = multiply(a,left_division(iPr_def_12,iPr_def_13)),
inference(demodulation,[status(thm)],[c_16311,c_3446]) ).
tcf(c_16342,plain,
multiply(a,left_division(iPr_def_12,iPr_def_13)) = right_inverse(c),
inference(light_normalisation,[status(thm)],[c_16341,c_989,c_3635]) ).
tcf(c_16381,plain,
left_division(right_inverse(c),a) = right_inverse(left_division(iPr_def_12,iPr_def_13)),
inference(superposition,[status(thm)],[c_16342,c_854]) ).
tcf(c_16398,plain,
multiply(c,a) = left_division(iPr_def_13,iPr_def_12),
inference(demodulation,[status(thm)],[c_16381,c_1221,c_3433]) ).
tcf(c_16399,plain,
left_division(iPr_def_13,iPr_def_12) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_16398,c_234]) ).
tcf(c_16431,plain,
multiply(iPr_def_13,iPr_def_14) = iPr_def_12,
inference(superposition,[status(thm)],[c_16399,c_61]) ).
tcf(c_16438,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_108,c_16431]) ).
tcf(c_16439,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_16438,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP202-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/10.46 % Computer : n014.cluster.edu
% 0.19/10.46 % Model : x86_64 x86_64
% 0.19/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.46 % Memory : 8046.5625MB
% 0.19/10.46 % OS : Linux 6.8.0-71-generic
% 0.19/10.46 % CPULimit : 300
% 0.19/10.46 % WCLimit : 300
% 0.19/10.46 % DateTime : Wed Sep 23 14:07:59 UTC 2026
% 0.19/10.47 % CPUTime :
% 0.19/10.47 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/10.50 Running UEQ theorem proving
% 0.22/10.50 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
% 0.22/10.51
% 0.22/10.51 % ======== iProver multi-core TPTP/SMT =========
% 0.22/10.51
% 0.22/10.51 % Detected problem language: tptp
% 0.22/10.53 % Proving...
% 8.49/11.83 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.49/11.83 % SZS status Started for theBenchmark.p
% 8.49/11.83 % SZS status Unsatisfiable for theBenchmark.p
% 8.49/11.83
% 8.49/11.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.49/11.83
% 8.49/11.83 % ------ iProver source info
% 8.49/11.83
% 8.49/11.83 % git: date: 2026-07-19 20:42:38 +0200
% 8.49/11.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.49/11.83 % git: non_committed_changes: false
% 8.49/11.83
% 8.49/11.83 % ------ Parsing...% successful
% 8.49/11.83
% 8.49/11.83
% 8.49/11.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.49/11.83
% 8.49/11.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.49/11.83
% 8.49/11.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.49/11.83
% 8.49/11.83 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.49/11.83 % ------ Proving...
% 8.49/11.83 % ------ Problem Properties
% 8.49/11.83
% 8.49/11.83 %
% 8.49/11.83 % clauses 16
% 8.49/11.83 % conjectures 1
% 8.49/11.83 % EPR 1
% 8.49/11.83 % Horn 16
% 8.49/11.83 % unary 16
% 8.49/11.83 % binary 0
% 8.49/11.83 % lits 16
% 8.49/11.83 % lits eq 16
% 8.49/11.83 % fd_pure 0
% 8.49/11.83 % fd_pseudo 0
% 8.49/11.83 % fd_cond 0
% 8.49/11.83 % fd_pseudo_cond 0
% 8.49/11.83 % AC symbols 0
% 8.49/11.83
% 8.49/11.83 % ------ Input Options Time Limit: Unbounded
% 8.49/11.83
% 8.49/11.83
% 8.49/11.83 % ------
% 8.49/11.83 % Current options:
% 8.49/11.83 % ------
% 8.49/11.83
% 8.49/11.83
% 8.49/11.83 %
% 8.49/11.83
% 8.49/11.83 % ------ Proving...
% 8.49/11.83 %
% 8.49/11.83
% 8.49/11.83 % SZS status Unsatisfiable for theBenchmark.p
% 8.49/11.83
% 8.49/11.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.49/11.83
% 8.49/11.83
%------------------------------------------------------------------------------