%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 01:35:15 PM UTC 2026
% Result : Theorem 2.59s 1.28s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 76 unt; 11 def)
% Number of atoms : 198 ( 100 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 21 ~; 12 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 47 !; 2 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f8,axiom,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f11,axiom,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
fof(f14,conjecture,
! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1)
& mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d)
& mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( mult(X0,mult(op_d,X1)) != mult(mult(X0,op_d),X1)
| mult(X0,mult(X1,op_d)) != mult(mult(X0,X1),op_d)
| mult(op_d,mult(X0,X1)) != mult(mult(op_d,X0),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( mult(sK0,mult(op_d,sK1)) != mult(mult(sK0,op_d),sK1)
| mult(sK0,mult(sK1,op_d)) != mult(mult(sK0,sK1),op_d)
| mult(op_d,mult(sK0,sK1)) != mult(mult(op_d,sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f31,plain,
( mult(sK0,mult(op_d,sK1)) != mult(mult(sK0,op_d),sK1)
| mult(sK0,mult(sK1,op_d)) != mult(mult(sK0,sK1),op_d)
| mult(op_d,mult(sK0,sK1)) != mult(mult(op_d,sK0),sK1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : mult(mult(op_c,X0),X1) = mult(op_c,mult(X0,X1)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_59,plain,
! [X0: $i] : ld(X0,mult(op_c,X0)) = op_d,
inference(cnf_transformation,[],[f28]) ).
tcf(c_62,negated_conjecture,
( ( mult(mult(sK0,sK1),op_d) != mult(sK0,mult(sK1,op_d)) )
| ( mult(mult(sK0,op_d),sK1) != mult(sK0,mult(op_d,sK1)) )
| ( mult(mult(op_d,sK0),sK1) != mult(op_d,mult(sK0,sK1)) ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_114,definition,
iPr_def_10 = mult(op_d,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_115,definition,
iPr_def_11 = mult(iPr_def_10,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_116,definition,
iPr_def_12 = mult(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_117,definition,
iPr_def_13 = mult(op_d,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_118,definition,
iPr_def_14 = mult(sK0,op_d),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_119,definition,
iPr_def_15 = mult(iPr_def_14,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_120,definition,
iPr_def_16 = mult(op_d,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_121,definition,
iPr_def_17 = mult(sK0,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_122,definition,
iPr_def_18 = mult(iPr_def_12,op_d),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_123,definition,
iPr_def_19 = mult(sK1,op_d),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_124,definition,
iPr_def_20 = mult(sK0,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_125,negated_conjecture,
( ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_15 != iPr_def_17 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_62,c_123,c_124,c_122,c_120,c_121,c_118,c_119,c_116,c_117,c_114,c_115]) ).
tcf(c_225,plain,
ld(sK0,iPr_def_12) = sK1,
inference(superposition,[status(thm)],[c_116,c_50]) ).
tcf(c_226,plain,
ld(op_d,iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_114,c_50]) ).
tcf(c_228,plain,
ld(op_d,iPr_def_16) = sK1,
inference(superposition,[status(thm)],[c_120,c_50]) ).
tcf(c_230,plain,
ld(iPr_def_10,iPr_def_11) = sK1,
inference(superposition,[status(thm)],[c_115,c_50]) ).
tcf(c_233,plain,
ld(sK0,iPr_def_17) = iPr_def_16,
inference(superposition,[status(thm)],[c_121,c_50]) ).
tcf(c_235,plain,
ld(sK0,iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_124,c_50]) ).
tcf(c_239,plain,
mult(sK0,sK1) = iPr_def_12,
inference(superposition,[status(thm)],[c_225,c_49]) ).
tcf(c_244,plain,
mult(iPr_def_10,sK1) = iPr_def_11,
inference(superposition,[status(thm)],[c_230,c_49]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_49,c_52]) ).
tcf(c_278,plain,
! [X0: $i] : ld(ld(op_c,X0),X0) = op_d,
inference(superposition,[status(thm)],[c_49,c_59]) ).
tcf(c_280,plain,
! [X0: $i] : mult(X0,op_d) = mult(op_c,X0),
inference(superposition,[status(thm)],[c_59,c_49]) ).
tcf(c_281,plain,
op_c = op_d,
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_286,plain,
ld(op_c,iPr_def_16) = sK1,
inference(demodulation,[status(thm)],[c_228,c_281]) ).
tcf(c_288,plain,
ld(op_c,iPr_def_10) = sK0,
inference(demodulation,[status(thm)],[c_226,c_281]) ).
tcf(c_289,plain,
mult(sK1,op_c) = iPr_def_19,
inference(demodulation,[status(thm)],[c_123,c_281]) ).
tcf(c_290,plain,
mult(iPr_def_12,op_c) = iPr_def_18,
inference(demodulation,[status(thm)],[c_122,c_281]) ).
tcf(c_292,plain,
mult(sK0,op_c) = iPr_def_14,
inference(demodulation,[status(thm)],[c_118,c_281]) ).
tcf(c_293,plain,
mult(op_c,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_117,c_281]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] : mult(op_c,mult(ld(op_c,X0),X1)) = mult(X0,X1),
inference(superposition,[status(thm)],[c_49,c_56]) ).
tcf(c_329,plain,
mult(sK0,iPr_def_16) = iPr_def_17,
inference(superposition,[status(thm)],[c_233,c_49]) ).
tcf(c_332,plain,
mult(sK0,iPr_def_19) = iPr_def_20,
inference(superposition,[status(thm)],[c_235,c_49]) ).
tcf(c_379,plain,
mult(sK0,mult(sK1,op_c)) = mult(iPr_def_12,op_c),
inference(superposition,[status(thm)],[c_239,c_57]) ).
tcf(c_381,plain,
mult(iPr_def_10,mult(sK1,op_c)) = mult(iPr_def_11,op_c),
inference(superposition,[status(thm)],[c_244,c_57]) ).
tcf(c_391,plain,
mult(iPr_def_10,iPr_def_19) = mult(iPr_def_11,op_c),
inference(light_normalisation,[status(thm)],[c_381,c_289]) ).
tcf(c_392,plain,
iPr_def_18 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_379,c_289,c_290,c_332]) ).
tcf(c_393,plain,
( ( iPr_def_15 != iPr_def_17 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_125,c_392]) ).
tcf(c_394,plain,
ld(sK0,iPr_def_18) = iPr_def_19,
inference(demodulation,[status(thm)],[c_235,c_392]) ).
tcf(c_714,plain,
iPr_def_13 = iPr_def_18,
inference(demodulation,[status(thm)],[c_293,c_281,c_280,c_290]) ).
tcf(c_728,plain,
! [X0: $i] : ld(ld(op_c,X0),X0) = op_c,
inference(light_normalisation,[status(thm)],[c_278,c_281]) ).
tcf(c_732,plain,
ld(sK1,iPr_def_16) = op_c,
inference(superposition,[status(thm)],[c_286,c_728]) ).
tcf(c_733,plain,
ld(sK0,iPr_def_10) = op_c,
inference(superposition,[status(thm)],[c_288,c_728]) ).
tcf(c_748,plain,
ld(sK0,iPr_def_13) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_394,c_714]) ).
tcf(c_749,plain,
mult(sK0,iPr_def_19) = iPr_def_13,
inference(superposition,[status(thm)],[c_748,c_49]) ).
tcf(c_768,plain,
mult(sK1,op_c) = iPr_def_16,
inference(superposition,[status(thm)],[c_732,c_49]) ).
tcf(c_769,plain,
iPr_def_16 = iPr_def_19,
inference(demodulation,[status(thm)],[c_289,c_768]) ).
tcf(c_774,plain,
mult(sK0,op_c) = iPr_def_10,
inference(superposition,[status(thm)],[c_733,c_49]) ).
tcf(c_775,plain,
iPr_def_10 = iPr_def_14,
inference(demodulation,[status(thm)],[c_292,c_774]) ).
tcf(c_781,plain,
mult(iPr_def_10,sK1) = iPr_def_15,
inference(demodulation,[status(thm)],[c_119,c_775]) ).
tcf(c_782,plain,
iPr_def_11 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_781,c_244]) ).
tcf(c_783,plain,
( ( iPr_def_11 != iPr_def_17 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_393,c_782]) ).
tcf(c_788,plain,
iPr_def_13 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_749,c_329,c_769]) ).
tcf(c_789,plain,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_783,c_788]) ).
tcf(c_793,plain,
mult(sK0,iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_121,c_788]) ).
tcf(c_854,plain,
! [X0: $i] : ld(op_c,X0) = rd(X0,op_c),
inference(superposition,[status(thm)],[c_728,c_252]) ).
tcf(c_877,plain,
mult(iPr_def_10,iPr_def_16) = mult(iPr_def_11,op_c),
inference(light_normalisation,[status(thm)],[c_391,c_769]) ).
tcf(c_879,plain,
rd(mult(iPr_def_10,iPr_def_16),op_c) = iPr_def_11,
inference(superposition,[status(thm)],[c_877,c_52]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i] : ld(op_c,mult(X0,X1)) = mult(ld(op_c,X0),X1),
inference(superposition,[status(thm)],[c_313,c_50]) ).
tcf(c_971,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_879,c_288,c_793,c_854,c_897]) ).
tcf(c_972,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_971,c_789]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP702+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 15:45:49 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.59/1.28 % SZS status Started for theBenchmark.p
% 2.59/1.28 % SZS status Theorem for theBenchmark.p
% 2.59/1.28
% 2.59/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.59/1.28
% 2.59/1.28 % ------ iProver source info
% 2.59/1.28
% 2.59/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.59/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.59/1.28 % git: non_committed_changes: false
% 2.59/1.28
% 2.59/1.28 % ------ Parsing...
% 2.59/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.59/1.28
% 2.59/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.59/1.28
% 2.59/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.59/1.28
% 2.59/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.59/1.28 % ------ Proving...
% 2.59/1.28 % ------ Problem Properties
% 2.59/1.28
% 2.59/1.28 %
% 2.59/1.28 % clauses 25
% 2.59/1.28 % conjectures 1
% 2.59/1.28 % EPR 1
% 2.59/1.28 % Horn 25
% 2.59/1.28 % unary 24
% 2.59/1.28 % binary 0
% 2.59/1.28 % lits 27
% 2.59/1.28 % lits eq 27
% 2.59/1.28 % fd_pure 0
% 2.59/1.28 % fd_pseudo 0
% 2.59/1.28 % fd_cond 0
% 2.59/1.28 % fd_pseudo_cond 0
% 2.59/1.28 % AC symbols 0
% 2.59/1.28
% 2.59/1.28 % ------ Schedule dynamic 5 is on
% 2.59/1.28
% 2.59/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.59/1.28
% 2.59/1.28
% 2.59/1.28 % ------
% 2.59/1.28 % Current options:
% 2.59/1.28 % ------
% 2.59/1.28
% 2.59/1.28
% 2.59/1.28 %
% 2.59/1.28
% 2.59/1.28 % ------ Proving...
% 2.59/1.28 %
% 2.59/1.28
% 2.59/1.28 % SZS status Theorem for theBenchmark.p
% 2.59/1.28
% 2.59/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.59/1.28
% 2.59/1.28
%------------------------------------------------------------------------------