%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 01:30:42 PM UTC 2026
% Result : Unsatisfiable 1.09s 1.29s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 62 unt; 13 def)
% Number of atoms : 197 ( 91 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 52 ( 31 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 50 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f3,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
( ( multiply(a4,b4) != multiply(b4,a4) )
| ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,definition,
iPr_def_10 = inverse(b2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_73,definition,
iPr_def_11 = multiply(iPr_def_10,b2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_74,definition,
iPr_def_12 = multiply(iPr_def_11,a2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_75,definition,
iPr_def_13 = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_76,definition,
iPr_def_14 = multiply(iPr_def_13,c3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_77,definition,
iPr_def_15 = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_78,definition,
iPr_def_16 = multiply(a3,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_79,definition,
iPr_def_17 = inverse(a1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_80,definition,
iPr_def_18 = multiply(iPr_def_17,a1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_81,definition,
iPr_def_19 = inverse(b1),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_82,definition,
iPr_def_20 = multiply(iPr_def_19,b1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_83,definition,
iPr_def_21 = multiply(a4,b4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_84,definition,
iPr_def_22 = multiply(b4,a4),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_85,negated_conjecture,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 )
| ( iPr_def_12 != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_84,c_83,c_81,c_82,c_79,c_80,c_77,c_78,c_75,c_76,c_72,c_73,c_74]) ).
tcf(c_153,plain,
! [X0: $i] : multiply(a3,multiply(multiply(inverse(iPr_def_13),X0),b3)) = X0,
inference(superposition,[status(thm)],[c_75,c_51]) ).
tcf(c_161,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(multiply(inverse(iPr_def_18),X0),a1)) = X0,
inference(superposition,[status(thm)],[c_80,c_51]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,multiply(multiply(inverse(X1),X2),multiply(multiply(inverse(multiply(X0,X3)),X1),X3))) = X2,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3),X2) = multiply(X0,multiply(X3,X1)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(multiply(inverse(iPr_def_13),X0)),X1),X0) = multiply(a3,multiply(X1,b3)),
inference(superposition,[status(thm)],[c_51,c_153]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[c_51,c_163]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),X1) = multiply(X2,X0),
inference(superposition,[status(thm)],[c_51,c_245]) ).
tcf(c_400,plain,
! [X0: $i] : multiply(multiply(iPr_def_17,X0),a1) = X0,
inference(superposition,[status(thm)],[c_79,c_245]) ).
tcf(c_401,plain,
! [X0: $i] : multiply(multiply(iPr_def_19,X0),b1) = X0,
inference(superposition,[status(thm)],[c_81,c_245]) ).
tcf(c_402,plain,
! [X0: $i] : multiply(multiply(iPr_def_10,X0),b2) = X0,
inference(superposition,[status(thm)],[c_72,c_245]) ).
tcf(c_419,plain,
multiply(iPr_def_18,a1) = a1,
inference(superposition,[status(thm)],[c_80,c_400]) ).
tcf(c_421,plain,
! [X0: $i] : multiply(multiply(inverse(iPr_def_18),X0),a1) = multiply(X0,a1),
inference(superposition,[status(thm)],[c_161,c_400]) ).
tcf(c_424,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(X0,a1)) = X0,
inference(demodulation,[status(thm)],[c_161,c_421]) ).
tcf(c_444,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(multiply(inverse(a1),X0),a1)) = X0,
inference(superposition,[status(thm)],[c_419,c_51]) ).
tcf(c_446,plain,
! [X0: $i] : multiply(iPr_def_18,X0) = X0,
inference(light_normalisation,[status(thm)],[c_444,c_79,c_400]) ).
tcf(c_458,plain,
multiply(iPr_def_20,b1) = b1,
inference(superposition,[status(thm)],[c_82,c_401]) ).
tcf(c_478,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(multiply(inverse(b1),X0),b1)) = X0,
inference(superposition,[status(thm)],[c_458,c_51]) ).
tcf(c_480,plain,
! [X0: $i] : multiply(iPr_def_20,X0) = X0,
inference(light_normalisation,[status(thm)],[c_478,c_81,c_401]) ).
tcf(c_512,plain,
multiply(iPr_def_11,b2) = b2,
inference(superposition,[status(thm)],[c_73,c_402]) ).
tcf(c_537,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(multiply(inverse(b2),X0),b2)) = X0,
inference(superposition,[status(thm)],[c_512,c_51]) ).
tcf(c_539,plain,
! [X0: $i] : multiply(iPr_def_11,X0) = X0,
inference(light_normalisation,[status(thm)],[c_537,c_72,c_402]) ).
tcf(c_540,plain,
a2 = iPr_def_12,
inference(demodulation,[status(thm)],[c_74,c_539]) ).
tcf(c_542,plain,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 )
| ( iPr_def_12 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_85,c_540]) ).
tcf(c_543,plain,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(equality_resolution_simp,[status(thm)],[c_542]) ).
tcf(c_565,plain,
multiply(iPr_def_17,a1) = iPr_def_18,
inference(superposition,[status(thm)],[c_446,c_424]) ).
tcf(c_566,plain,
multiply(iPr_def_17,a1) = iPr_def_20,
inference(superposition,[status(thm)],[c_480,c_424]) ).
tcf(c_567,plain,
multiply(iPr_def_17,a1) = iPr_def_11,
inference(superposition,[status(thm)],[c_539,c_424]) ).
tcf(c_571,plain,
iPr_def_18 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_566,c_80]) ).
tcf(c_574,plain,
iPr_def_11 = iPr_def_18,
inference(demodulation,[status(thm)],[c_80,c_567]) ).
tcf(c_575,plain,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_14 != iPr_def_16 )
| ( iPr_def_11 != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_543,c_574]) ).
tcf(c_587,plain,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_575,c_543,c_571]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(demodulation,[status(thm)],[c_164,c_398]) ).
tcf(c_625,plain,
! [X0: $i] : multiply(a3,multiply(X0,b3)) = multiply(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_75,c_592]) ).
tcf(c_626,plain,
! [X0: $i] : multiply(b3,multiply(X0,c3)) = multiply(X0,iPr_def_15),
inference(superposition,[status(thm)],[c_77,c_592]) ).
tcf(c_627,plain,
! [X0: $i] : multiply(a4,multiply(X0,b4)) = multiply(X0,iPr_def_21),
inference(superposition,[status(thm)],[c_83,c_592]) ).
tcf(c_693,plain,
! [X0: $i] : multiply(X0,multiply(iPr_def_17,a1)) = X0,
inference(superposition,[status(thm)],[c_592,c_424]) ).
tcf(c_695,plain,
! [X0: $i] : multiply(X0,iPr_def_11) = X0,
inference(light_normalisation,[status(thm)],[c_693,c_565,c_574]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(multiply(X0,iPr_def_11)),X1)) = X1,
inference(superposition,[status(thm)],[c_695,c_51]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(light_normalisation,[status(thm)],[c_881,c_695]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),X1) = multiply(X0,X2),
inference(superposition,[status(thm)],[c_51,c_889]) ).
tcf(c_1091,plain,
! [X0: $i] : multiply(X0,iPr_def_13) = multiply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_177,c_625,c_985]) ).
tcf(c_1210,plain,
multiply(inverse(b3),iPr_def_15) = c3,
inference(superposition,[status(thm)],[c_626,c_889]) ).
tcf(c_1345,plain,
multiply(c3,b3) = iPr_def_15,
inference(superposition,[status(thm)],[c_1210,c_245]) ).
tcf(c_1368,plain,
multiply(inverse(a4),iPr_def_21) = b4,
inference(superposition,[status(thm)],[c_627,c_889]) ).
tcf(c_1465,plain,
multiply(a3,iPr_def_15) = multiply(c3,iPr_def_13),
inference(superposition,[status(thm)],[c_1345,c_625]) ).
tcf(c_1466,plain,
multiply(c3,iPr_def_13) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1465,c_78]) ).
tcf(c_1507,plain,
iPr_def_14 = iPr_def_16,
inference(demodulation,[status(thm)],[c_1466,c_76,c_1091]) ).
tcf(c_1508,plain,
( ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_14 != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_587,c_1507]) ).
tcf(c_1510,plain,
iPr_def_21 != iPr_def_22,
inference(equality_resolution_simp,[status(thm)],[c_1508]) ).
tcf(c_1519,plain,
multiply(b4,a4) = iPr_def_21,
inference(superposition,[status(thm)],[c_1368,c_245]) ).
tcf(c_1522,plain,
iPr_def_21 = iPr_def_22,
inference(demodulation,[status(thm)],[c_84,c_1519]) ).
tcf(c_1523,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1522,c_1510]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:24:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.09/1.29 % SZS status Started for theBenchmark.p
% 1.09/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.09/1.29
% 1.09/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.09/1.29
% 1.09/1.29 % ------ iProver source info
% 1.09/1.29
% 1.09/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.09/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.09/1.29 % git: non_committed_changes: false
% 1.09/1.29
% 1.09/1.29 % ------ Parsing...% successful
% 1.09/1.29
% 1.09/1.29
% 1.09/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.09/1.29
% 1.09/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.09/1.29
% 1.09/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.09/1.29
% 1.09/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.09/1.29 % ------ Proving...
% 1.09/1.29 % ------ Problem Properties
% 1.09/1.29
% 1.09/1.29 %
% 1.09/1.29 % clauses 15
% 1.09/1.29 % conjectures 1
% 1.09/1.29 % EPR 1
% 1.09/1.29 % Horn 15
% 1.09/1.29 % unary 14
% 1.09/1.29 % binary 0
% 1.09/1.29 % lits 18
% 1.09/1.29 % lits eq 18
% 1.09/1.29 % fd_pure 0
% 1.09/1.29 % fd_pseudo 0
% 1.09/1.29 % fd_cond 0
% 1.09/1.29 % fd_pseudo_cond 0
% 1.09/1.29 % AC symbols 0
% 1.09/1.29
% 1.09/1.29 % ------ Schedule dynamic 5 is on
% 1.09/1.29
% 1.09/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.09/1.29
% 1.09/1.29
% 1.09/1.29 % ------
% 1.09/1.29 % Current options:
% 1.09/1.29 % ------
% 1.09/1.29
% 1.09/1.29
% 1.09/1.29 %
% 1.09/1.29
% 1.09/1.29 % ------ Proving...
% 1.09/1.29 %
% 1.09/1.29
% 1.09/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.09/1.29
% 1.09/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.09/1.29
% 1.09/1.29
%------------------------------------------------------------------------------