%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP665+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 : n012.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 01:35:08 PM UTC 2026
% Result : Theorem 1.47s 0.96s
% Output : CNFRefutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 62 ( 50 unt; 6 def)
% Number of atoms : 144 ( 82 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 28 ~; 17 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 56 !; 2 ?; 26 :)
% 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(f7,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f10,conjecture,
! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
? [X0,X1] :
( mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c))
| mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f13,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f14,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X2,X0,X1] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X2,X0,X1] : mult(mult(X2,X1),X0) = mult(mult(X2,X0),ld(X0,mult(X1,X0))),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f23,plain,
( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c))
| mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1))
| mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,X1),ld(X1,mult(X2,X1))) = mult(mult(X0,X2),X1),
inference(cnf_transformation,[],[f21]) ).
tcf(c_57,plain,
! [X0: $i] : mult(X0,op_c) = mult(op_c,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_58,negated_conjecture,
( ( mult(mult(sK0,sK1),op_c) != mult(sK0,mult(sK1,op_c)) )
| ( mult(mult(sK0,op_c),sK1) != mult(sK0,mult(op_c,sK1)) )
| ( mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_92,plain,
( ( mult(op_c,mult(sK0,sK1)) != mult(sK0,mult(op_c,sK1)) )
| ( mult(mult(op_c,sK0),sK1) != mult(sK0,mult(op_c,sK1)) )
| ( mult(mult(op_c,sK0),sK1) != mult(op_c,mult(sK0,sK1)) ) ),
inference(demodulation,[status(thm)],[c_58,c_57]) ).
tcf(c_101,definition,
iPr_def_10 = mult(op_c,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_102,definition,
iPr_def_11 = mult(iPr_def_10,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_103,definition,
iPr_def_12 = mult(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_104,definition,
iPr_def_13 = mult(op_c,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_105,definition,
iPr_def_14 = mult(op_c,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_106,definition,
iPr_def_15 = mult(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_107,plain,
( ( iPr_def_13 != iPr_def_15 )
| ( iPr_def_11 != iPr_def_15 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_92,c_105,c_106,c_103,c_104,c_101,c_102]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_162,plain,
( ( iPr_def_13 != iPr_def_15 )
| ( iPr_def_11 != iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_109]) ).
tcf(c_173,plain,
( ( iPr_def_13 != iPr_def_15 )
| ( iPr_def_11 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_162]) ).
tcf(c_177,plain,
mult(iPr_def_12,op_c) = iPr_def_13,
inference(demodulation,[status(thm)],[c_104,c_57]) ).
tcf(c_183,plain,
ld(sK0,iPr_def_12) = sK1,
inference(superposition,[status(thm)],[c_103,c_50]) ).
tcf(c_184,plain,
ld(op_c,iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_101,c_50]) ).
tcf(c_186,plain,
ld(iPr_def_10,iPr_def_11) = sK1,
inference(superposition,[status(thm)],[c_102,c_50]) ).
tcf(c_187,plain,
ld(sK0,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_106,c_50]) ).
tcf(c_210,plain,
mult(sK0,sK1) = iPr_def_12,
inference(superposition,[status(thm)],[c_183,c_49]) ).
tcf(c_213,plain,
mult(op_c,sK0) = iPr_def_10,
inference(superposition,[status(thm)],[c_184,c_49]) ).
tcf(c_219,plain,
mult(iPr_def_10,sK1) = iPr_def_11,
inference(superposition,[status(thm)],[c_186,c_49]) ).
tcf(c_220,plain,
mult(sK0,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_187,c_49]) ).
tcf(c_231,plain,
! [X0: $i] : rd(mult(op_c,X0),op_c) = X0,
inference(superposition,[status(thm)],[c_57,c_52]) ).
tcf(c_232,plain,
! [X0: $i] : ld(X0,mult(op_c,X0)) = op_c,
inference(superposition,[status(thm)],[c_57,c_50]) ).
tcf(c_266,plain,
! [X0: $i] : mult(rd(mult(op_c,X0),op_c),iPr_def_14) = mult(op_c,mult(X0,sK1)),
inference(superposition,[status(thm)],[c_105,c_55]) ).
tcf(c_274,plain,
! [X0: $i] : mult(op_c,mult(X0,sK1)) = mult(X0,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_266,c_231]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i] : mult(mult(X0,X1),op_c) = mult(mult(X0,op_c),X1),
inference(superposition,[status(thm)],[c_232,c_56]) ).
tcf(c_575,plain,
mult(op_c,iPr_def_12) = mult(sK0,iPr_def_14),
inference(superposition,[status(thm)],[c_210,c_274]) ).
tcf(c_583,plain,
! [X0: $i] : ld(mult(X0,sK1),mult(X0,iPr_def_14)) = op_c,
inference(superposition,[status(thm)],[c_274,c_232]) ).
tcf(c_584,plain,
mult(op_c,iPr_def_12) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_575,c_220]) ).
tcf(c_602,plain,
iPr_def_13 = iPr_def_15,
inference(demodulation,[status(thm)],[c_584,c_57,c_177]) ).
tcf(c_606,plain,
mult(sK0,iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_106,c_602]) ).
tcf(c_607,plain,
( ( iPr_def_13 != iPr_def_13 )
| ( iPr_def_11 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_173,c_602]) ).
tcf(c_608,plain,
iPr_def_11 != iPr_def_13,
inference(equality_resolution_simp,[status(thm)],[c_607]) ).
tcf(c_1035,plain,
! [X0: $i] : mult(mult(X0,sK1),op_c) = mult(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_583,c_49]) ).
tcf(c_1509,plain,
! [X0: $i] : mult(mult(X0,op_c),sK1) = mult(X0,iPr_def_14),
inference(demodulation,[status(thm)],[c_1035,c_515]) ).
tcf(c_1512,plain,
! [X0: $i] : mult(mult(op_c,X0),sK1) = mult(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_57,c_1509]) ).
tcf(c_2018,plain,
mult(sK0,iPr_def_14) = mult(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_213,c_1512]) ).
tcf(c_2034,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2018,c_219,c_606]) ).
tcf(c_2035,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2034,c_608]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 15:35:18 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.06/0.33
% 0.06/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.06/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 1.47/0.96 % SZS status Started for theBenchmark.p
% 1.47/0.96 % SZS status Theorem for theBenchmark.p
% 1.47/0.96
% 1.47/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.47/0.96
% 1.47/0.96 % ------ iProver source info
% 1.47/0.96
% 1.47/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 1.47/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.47/0.96 % git: non_committed_changes: false
% 1.47/0.96
% 1.47/0.96 % ------ Parsing...
% 1.47/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.47/0.96
% 1.47/0.96 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.47/0.96
% 1.47/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.47/0.96
% 1.47/0.96 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.47/0.96 % ------ Proving...
% 1.47/0.96 % ------ Problem Properties
% 1.47/0.96
% 1.47/0.96 %
% 1.47/0.96 % clauses 16
% 1.47/0.96 % conjectures 0
% 1.47/0.96 % EPR 1
% 1.47/0.96 % Horn 16
% 1.47/0.96 % unary 15
% 1.47/0.96 % binary 0
% 1.47/0.96 % lits 18
% 1.47/0.96 % lits eq 18
% 1.47/0.96 % fd_pure 0
% 1.47/0.96 % fd_pseudo 0
% 1.47/0.96 % fd_cond 0
% 1.47/0.96 % fd_pseudo_cond 0
% 1.47/0.96 % AC symbols 0
% 1.47/0.96
% 1.47/0.96 % ------ Schedule dynamic 5 is on
% 1.47/0.96
% 1.47/0.96 % ------ no conjectures: strip conj schedule
% 1.47/0.96
% 1.47/0.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.47/0.96
% 1.47/0.96
% 1.47/0.96 % ------
% 1.47/0.96 % Current options:
% 1.47/0.96 % ------
% 1.47/0.96
% 1.47/0.96
% 1.47/0.96 %
% 1.47/0.96
% 1.47/0.96 % ------ Proving...
% 1.47/0.96 %
% 1.47/0.96
% 1.47/0.96 % SZS status Theorem for theBenchmark.p
% 1.47/0.96
% 1.47/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.47/0.96
% 1.47/0.96
%------------------------------------------------------------------------------