%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 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 01:31:48 PM UTC 2026
% Result : Unsatisfiable 21.74s 4.23s
% Output : CNFRefutation 21.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 84 unt; 6 def)
% Number of atoms : 146 ( 83 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 : 102 ( 0 sgn 102 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [X0,X1] : right_division(multiply(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
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),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang3) ).
fof(f12,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang4) ).
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_64,plain,
! [X0: $i,X1: $i] : right_division(multiply(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f6]) ).
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(x,y),multiply(z,x)) != multiply(x,multiply(multiply(y,z),x)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,definition,
iPr_def_10 = multiply(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_103,definition,
iPr_def_11 = multiply(z,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_104,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_105,definition,
iPr_def_13 = multiply(y,z),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_106,definition,
iPr_def_14 = multiply(iPr_def_13,x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_107,definition,
iPr_def_15 = multiply(x,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_108,negated_conjecture,
iPr_def_12 != iPr_def_15,
inference(demodulation,[status(thm)],[c_68,c_105,c_106,c_107,c_103,c_102,c_104]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(X0,X1),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_111,plain,
! [X0: $i] : multiply(X0,right_inverse(X0)) = identity,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : right_division(multiply(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] : multiply(right_division(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : multiply(X0,left_division(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_116,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,identity))) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_109,c_116]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_436,c_116]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_division(X0,X1),X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_115,c_443]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] : multiply(left_division(X0,X1),X0) = left_division(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_498,c_114]) ).
tcf(c_1792,plain,
right_division(iPr_def_13,z) = y,
inference(superposition,[status(thm)],[c_105,c_112]) ).
tcf(c_1793,plain,
right_division(iPr_def_10,y) = x,
inference(superposition,[status(thm)],[c_102,c_112]) ).
tcf(c_1794,plain,
right_division(iPr_def_11,x) = z,
inference(superposition,[status(thm)],[c_103,c_112]) ).
tcf(c_1795,plain,
right_division(iPr_def_12,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_104,c_112]) ).
tcf(c_1796,plain,
right_division(iPr_def_14,x) = iPr_def_13,
inference(superposition,[status(thm)],[c_106,c_112]) ).
tcf(c_1797,plain,
right_division(iPr_def_15,iPr_def_14) = x,
inference(superposition,[status(thm)],[c_107,c_112]) ).
tcf(c_1812,plain,
multiply(x,y) = iPr_def_10,
inference(superposition,[status(thm)],[c_1793,c_113]) ).
tcf(c_1813,plain,
multiply(z,x) = iPr_def_11,
inference(superposition,[status(thm)],[c_1794,c_113]) ).
tcf(c_1814,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_1795,c_113]) ).
tcf(c_1815,plain,
multiply(iPr_def_13,x) = iPr_def_14,
inference(superposition,[status(thm)],[c_1796,c_113]) ).
tcf(c_1816,plain,
multiply(x,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_1797,c_113]) ).
tcf(c_1831,plain,
left_division(x,iPr_def_10) = y,
inference(superposition,[status(thm)],[c_1812,c_114]) ).
tcf(c_1865,plain,
! [X0: $i,X1: $i] : right_division(X0,left_division(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_115,c_112]) ).
tcf(c_1899,plain,
! [X0: $i,X1: $i] : multiply(left_division(X0,right_division(X1,X0)),X0) = left_division(X0,X1),
inference(superposition,[status(thm)],[c_113,c_913]) ).
tcf(c_1914,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_division(X0,X1),X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_913,c_115]) ).
tcf(c_2063,plain,
! [X0: $i,X1: $i] : left_division(X0,right_division(X1,X0)) = right_division(left_division(X0,X1),X0),
inference(superposition,[status(thm)],[c_1899,c_112]) ).
tcf(c_2082,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_114,c_1914]) ).
tcf(c_2377,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(light_normalisation,[status(thm)],[c_109,c_2082]) ).
tcf(c_2394,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(right_division(X1,X0),multiply(X0,X2))) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c_113,c_2377]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(X0,multiply(right_inverse(X0),X1))) = multiply(multiply(right_inverse(X0),identity),X1),
inference(superposition,[status(thm)],[c_111,c_2377]) ).
tcf(c_2404,plain,
! [X0: $i] : multiply(x,multiply(iPr_def_13,multiply(x,X0))) = multiply(multiply(x,iPr_def_14),X0),
inference(superposition,[status(thm)],[c_1815,c_2377]) ).
tcf(c_2436,plain,
! [X0: $i] : multiply(x,multiply(iPr_def_13,multiply(x,X0))) = multiply(iPr_def_15,X0),
inference(demodulation,[status(thm)],[c_2404,c_1816]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(X0,multiply(right_inverse(X0),X1))) = multiply(right_inverse(X0),X1),
inference(demodulation,[status(thm)],[c_2395,c_116]) ).
tcf(c_2513,plain,
! [X0: $i,X1: $i] : left_division(X0,right_division(multiply(X0,X1),X0)) = right_division(X1,X0),
inference(superposition,[status(thm)],[c_114,c_2063]) ).
tcf(c_2605,plain,
! [X0: $i,X1: $i] : left_division(multiply(X0,X1),multiply(X0,multiply(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_2082,c_114]) ).
tcf(c_3314,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(x,X0)) = left_division(x,multiply(iPr_def_15,X0)),
inference(superposition,[status(thm)],[c_2436,c_114]) ).
tcf(c_3963,plain,
! [X0: $i,X1: $i] : multiply(X0,right_division(X1,X0)) = right_division(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_2513,c_115]) ).
tcf(c_4700,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(x,left_division(iPr_def_15,X0))) = left_division(x,X0),
inference(superposition,[status(thm)],[c_115,c_3314]) ).
tcf(c_6382,plain,
! [X0: $i] : multiply(x,left_division(iPr_def_15,X0)) = left_division(iPr_def_13,left_division(x,X0)),
inference(superposition,[status(thm)],[c_4700,c_114]) ).
tcf(c_7498,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(right_division(X0,X1),multiply(X1,X2)) = left_division(X1,multiply(multiply(X1,X0),X2)),
inference(superposition,[status(thm)],[c_2394,c_114]) ).
tcf(c_9866,plain,
multiply(x,left_division(iPr_def_15,iPr_def_10)) = left_division(iPr_def_13,y),
inference(superposition,[status(thm)],[c_1831,c_6382]) ).
tcf(c_9893,plain,
right_division(left_division(iPr_def_13,y),left_division(iPr_def_15,iPr_def_10)) = x,
inference(superposition,[status(thm)],[c_9866,c_112]) ).
tcf(c_14032,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_115,c_2439]) ).
tcf(c_14916,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),X1) = left_division(X0,X1),
inference(superposition,[status(thm)],[c_115,c_14032]) ).
tcf(c_15023,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(right_inverse(X1),multiply(multiply(X1,X0),right_inverse(X1)))) = right_inverse(X1),
inference(superposition,[status(thm)],[c_14032,c_2605]) ).
tcf(c_15025,plain,
! [X0: $i,X1: $i] : multiply(right_inverse(X0),multiply(multiply(X0,X1),right_inverse(X0))) = multiply(X1,right_inverse(X0)),
inference(superposition,[status(thm)],[c_14032,c_2082]) ).
tcf(c_15027,plain,
! [X0: $i,X1: $i] : left_division(right_inverse(X0),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_14032,c_114]) ).
tcf(c_15110,plain,
! [X0: $i,X1: $i] : left_division(X0,multiply(multiply(X0,X1),right_inverse(X0))) = multiply(X1,right_inverse(X0)),
inference(demodulation,[status(thm)],[c_15025,c_14916]) ).
tcf(c_15111,plain,
! [X0: $i,X1: $i] : multiply(X0,right_inverse(X1)) = right_division(X0,X1),
inference(demodulation,[status(thm)],[c_15110,c_116,c_111,c_7498]) ).
tcf(c_15112,plain,
! [X0: $i,X1: $i] : left_division(X0,left_division(X1,right_division(multiply(X1,X0),X1))) = right_inverse(X1),
inference(demodulation,[status(thm)],[c_15023,c_15111,c_14916]) ).
tcf(c_15113,plain,
! [X0: $i,X1: $i] : left_division(X0,right_division(X0,X1)) = right_inverse(X1),
inference(demodulation,[status(thm)],[c_15112,c_114,c_3963]) ).
tcf(c_16784,plain,
left_division(iPr_def_13,y) = right_inverse(z),
inference(superposition,[status(thm)],[c_1792,c_15113]) ).
tcf(c_16790,plain,
! [X0: $i,X1: $i] : right_inverse(left_division(X0,X1)) = left_division(X1,X0),
inference(superposition,[status(thm)],[c_1865,c_15113]) ).
tcf(c_16845,plain,
left_division(left_division(iPr_def_13,y),x) = right_inverse(left_division(iPr_def_15,iPr_def_10)),
inference(superposition,[status(thm)],[c_9893,c_15113]) ).
tcf(c_16885,plain,
left_division(right_inverse(z),x) = left_division(iPr_def_10,iPr_def_15),
inference(demodulation,[status(thm)],[c_16845,c_16784,c_16790]) ).
tcf(c_16886,plain,
left_division(iPr_def_10,iPr_def_15) = iPr_def_11,
inference(demodulation,[status(thm)],[c_16885,c_1813,c_15027]) ).
tcf(c_17166,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_15,
inference(superposition,[status(thm)],[c_16886,c_115]) ).
tcf(c_17170,plain,
iPr_def_12 = iPr_def_15,
inference(demodulation,[status(thm)],[c_17166,c_1814]) ).
tcf(c_17171,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_17170,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP205-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:08:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running UEQ theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 21.74/4.23 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 21.74/4.23 % SZS status Started for theBenchmark.p
% 21.74/4.23 % SZS status Unsatisfiable for theBenchmark.p
% 21.74/4.23
% 21.74/4.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.74/4.23
% 21.74/4.23 % ------ iProver source info
% 21.74/4.23
% 21.74/4.23 % git: date: 2026-07-19 20:42:38 +0200
% 21.74/4.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.74/4.23 % git: non_committed_changes: false
% 21.74/4.23
% 21.74/4.23 % ------ Parsing...% successful
% 21.74/4.23
% 21.74/4.23
% 21.74/4.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.74/4.23
% 21.74/4.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 21.74/4.23
% 21.74/4.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.74/4.23
% 21.74/4.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 21.74/4.23 % ------ Proving...
% 21.74/4.23 % ------ Problem Properties
% 21.74/4.23
% 21.74/4.23 %
% 21.74/4.23 % clauses 16
% 21.74/4.23 % conjectures 1
% 21.74/4.23 % EPR 1
% 21.74/4.23 % Horn 16
% 21.74/4.23 % unary 16
% 21.74/4.23 % binary 0
% 21.74/4.23 % lits 16
% 21.74/4.23 % lits eq 16
% 21.74/4.23 % fd_pure 0
% 21.74/4.23 % fd_pseudo 0
% 21.74/4.23 % fd_cond 0
% 21.74/4.23 % fd_pseudo_cond 0
% 21.74/4.23 % AC symbols 0
% 21.74/4.23
% 21.74/4.23 % ------ Input Options Time Limit: Unbounded
% 21.74/4.23
% 21.74/4.23
% 21.74/4.23 % ------
% 21.74/4.23 % Current options:
% 21.74/4.23 % ------
% 21.74/4.23
% 21.74/4.23
% 21.74/4.23 %
% 21.74/4.23
% 21.74/4.23 % ------ Proving...
% 21.74/4.23 %
% 21.74/4.23
% 21.74/4.23 % SZS status Unsatisfiable for theBenchmark.p
% 21.74/4.23
% 21.74/4.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.74/4.23
% 21.74/4.23
%------------------------------------------------------------------------------