%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP660+3 : 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 : n020.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 01:35:07 PM UTC 2026
% Result : Theorem 5.89s 1.59s
% Output : CNFRefutation 5.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of formulae : 87 ( 79 unt; 3 def)
% Number of atoms : 244 ( 94 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 75 !; 2 ?; 49 :)
% 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(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0,X1,X2] : mult(mult(mult(X2,X1),X0),X2) = mult(X2,mult(X1,mult(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( mult(ld(X1,X1),X0) = X0
& mult(X0,ld(X1,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( mult(ld(X1,X1),X0) != X0
| mult(X0,ld(X1,X1)) != X0 ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( sK0 != mult(ld(sK1,sK1),sK0)
| sK0 != mult(sK0,ld(sK1,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
fof(f10,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(mult(mult(X2,X1),X0),X2) = mult(X2,mult(X1,mult(X0,X2))),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
( sK0 != mult(ld(sK1,sK1),sK0)
| sK0 != mult(sK0,ld(sK1,sK1)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[],[f11]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
inference(cnf_transformation,[],[f14]) ).
tcf(c_54,negated_conjecture,
( ( mult(sK0,ld(sK1,sK1)) != sK0 )
| ( mult(ld(sK1,sK1),sK0) != sK0 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_81,definition,
iPr_def_10 = ld(sK1,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_82,definition,
iPr_def_11 = mult(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_83,definition,
iPr_def_12 = mult(sK0,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_84,negated_conjecture,
( ( iPr_def_12 != sK0 )
| ( iPr_def_11 != sK0 ) ),
inference(demodulation,[status(thm)],[c_54,c_83,c_81,c_82]) ).
tcf(c_140,plain,
mult(sK1,iPr_def_10) = sK1,
inference(superposition,[status(thm)],[c_81,c_49]) ).
tcf(c_141,plain,
ld(iPr_def_10,iPr_def_11) = sK0,
inference(superposition,[status(thm)],[c_82,c_50]) ).
tcf(c_142,plain,
ld(sK0,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_83,c_50]) ).
tcf(c_145,plain,
mult(sK0,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_142,c_49]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_51,c_50]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[status(thm)],[c_49,c_52]) ).
tcf(c_150,plain,
rd(iPr_def_12,iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_83,c_52]) ).
tcf(c_151,plain,
rd(sK1,iPr_def_10) = sK1,
inference(superposition,[status(thm)],[c_140,c_52]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(X1,mult(ld(mult(X0,X1),X2),X0))) = mult(X2,X0),
inference(superposition,[status(thm)],[c_49,c_53]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(X0,X1),mult(X2,X0))) = mult(mult(X1,X2),X0),
inference(superposition,[status(thm)],[c_49,c_53]) ).
tcf(c_158,plain,
! [X0: $i] : mult(iPr_def_10,mult(sK0,mult(X0,iPr_def_10))) = mult(mult(iPr_def_11,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_82,c_53]) ).
tcf(c_160,plain,
! [X0: $i] : mult(sK1,mult(iPr_def_10,mult(X0,sK1))) = mult(mult(sK1,X0),sK1),
inference(superposition,[status(thm)],[c_140,c_53]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] : ld(mult(mult(X0,X1),X2),mult(X0,mult(X1,mult(X2,X0)))) = X0,
inference(superposition,[status(thm)],[c_53,c_50]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(mult(X1,X0),X2),X1)) = ld(X1,mult(X2,X1)),
inference(superposition,[status(thm)],[c_153,c_50]) ).
tcf(c_358,plain,
! [X0: $i] : rd(mult(mult(sK1,X0),sK1),mult(iPr_def_10,mult(X0,sK1))) = sK1,
inference(superposition,[status(thm)],[c_160,c_52]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,rd(X1,X2)),X2) = mult(X2,mult(ld(X2,X0),X1)),
inference(superposition,[status(thm)],[c_51,c_155]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i] : ld(X0,mult(mult(X1,X2),X0)) = mult(ld(X0,X1),mult(X2,X0)),
inference(superposition,[status(thm)],[c_155,c_50]) ).
tcf(c_613,plain,
rd(mult(sK1,sK1),mult(iPr_def_10,mult(iPr_def_10,sK1))) = sK1,
inference(superposition,[status(thm)],[c_140,c_358]) ).
tcf(c_625,plain,
ld(sK1,mult(sK1,sK1)) = mult(iPr_def_10,mult(iPr_def_10,sK1)),
inference(superposition,[status(thm)],[c_613,c_146]) ).
tcf(c_627,plain,
mult(iPr_def_10,mult(iPr_def_10,sK1)) = sK1,
inference(demodulation,[status(thm)],[c_625,c_50]) ).
tcf(c_630,plain,
rd(sK1,mult(iPr_def_10,sK1)) = iPr_def_10,
inference(superposition,[status(thm)],[c_627,c_52]) ).
tcf(c_631,plain,
ld(iPr_def_10,sK1) = mult(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_627,c_50]) ).
tcf(c_1964,plain,
! [X0: $i] : ld(mult(mult(iPr_def_10,X0),sK1),mult(iPr_def_10,mult(X0,sK1))) = iPr_def_10,
inference(superposition,[status(thm)],[c_140,c_163]) ).
tcf(c_4046,plain,
ld(mult(mult(iPr_def_10,iPr_def_10),sK1),sK1) = iPr_def_10,
inference(superposition,[status(thm)],[c_627,c_1964]) ).
tcf(c_4048,plain,
! [X0: $i] : ld(mult(mult(iPr_def_10,rd(X0,sK1)),sK1),mult(iPr_def_10,X0)) = iPr_def_10,
inference(superposition,[status(thm)],[c_51,c_1964]) ).
tcf(c_4090,plain,
mult(mult(iPr_def_10,iPr_def_10),sK1) = rd(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_4046,c_148]) ).
tcf(c_4091,plain,
mult(mult(iPr_def_10,iPr_def_10),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_4090,c_151]) ).
tcf(c_4098,plain,
mult(iPr_def_10,iPr_def_10) = rd(sK1,sK1),
inference(superposition,[status(thm)],[c_4091,c_52]) ).
tcf(c_4899,plain,
! [X0: $i] : ld(mult(sK1,mult(ld(sK1,iPr_def_10),X0)),mult(iPr_def_10,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4048,c_515]) ).
tcf(c_4901,plain,
! [X0: $i] : ld(mult(sK1,X0),mult(iPr_def_10,ld(ld(sK1,iPr_def_10),X0))) = iPr_def_10,
inference(superposition,[status(thm)],[c_49,c_4899]) ).
tcf(c_4920,plain,
! [X0: $i] : mult(sK1,mult(ld(sK1,iPr_def_10),X0)) = rd(mult(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_4899,c_148]) ).
tcf(c_5657,plain,
! [X0: $i] : mult(iPr_def_10,ld(ld(sK1,iPr_def_10),X0)) = mult(mult(sK1,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_4901,c_49]) ).
tcf(c_5909,plain,
! [X0: $i] : rd(rd(mult(iPr_def_10,X0),iPr_def_10),mult(ld(sK1,iPr_def_10),X0)) = sK1,
inference(superposition,[status(thm)],[c_4920,c_52]) ).
tcf(c_6721,plain,
! [X0: $i] : ld(iPr_def_10,mult(mult(sK1,X0),iPr_def_10)) = ld(ld(sK1,iPr_def_10),X0),
inference(superposition,[status(thm)],[c_5657,c_50]) ).
tcf(c_7829,plain,
rd(iPr_def_10,mult(ld(sK1,iPr_def_10),iPr_def_10)) = sK1,
inference(superposition,[status(thm)],[c_52,c_5909]) ).
tcf(c_7913,plain,
mult(ld(sK1,iPr_def_10),iPr_def_10) = ld(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_7829,c_146]) ).
tcf(c_7939,plain,
ld(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_7913,c_50]) ).
tcf(c_8922,plain,
! [X0: $i] : mult(mult(iPr_def_10,sK1),mult(X0,iPr_def_10)) = ld(ld(sK1,iPr_def_10),X0),
inference(demodulation,[status(thm)],[c_6721,c_533,c_631]) ).
tcf(c_8933,plain,
ld(ld(sK1,iPr_def_10),ld(sK1,iPr_def_10)) = mult(mult(iPr_def_10,sK1),ld(sK1,iPr_def_10)),
inference(superposition,[status(thm)],[c_7913,c_8922]) ).
tcf(c_8951,plain,
mult(mult(iPr_def_10,sK1),ld(sK1,iPr_def_10)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8933,c_7939]) ).
tcf(c_9203,plain,
rd(iPr_def_10,ld(sK1,iPr_def_10)) = mult(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_8951,c_52]) ).
tcf(c_9224,plain,
mult(iPr_def_10,sK1) = sK1,
inference(demodulation,[status(thm)],[c_9203,c_148]) ).
tcf(c_9241,plain,
rd(sK1,sK1) = iPr_def_10,
inference(demodulation,[status(thm)],[c_630,c_9224]) ).
tcf(c_9249,plain,
mult(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4098,c_9241]) ).
tcf(c_9435,plain,
! [X0: $i] : mult(iPr_def_10,mult(ld(iPr_def_10,X0),iPr_def_10)) = mult(mult(X0,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_9249,c_155]) ).
tcf(c_9445,plain,
mult(mult(iPr_def_11,iPr_def_10),iPr_def_10) = mult(iPr_def_10,mult(sK0,iPr_def_10)),
inference(superposition,[status(thm)],[c_9249,c_158]) ).
tcf(c_9466,plain,
mult(mult(iPr_def_11,iPr_def_10),iPr_def_10) = mult(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_9445,c_145]) ).
tcf(c_10738,plain,
! [X0: $i] : mult(iPr_def_10,mult(ld(iPr_def_10,X0),iPr_def_10)) = ld(iPr_def_10,mult(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_9249,c_297]) ).
tcf(c_10827,plain,
! [X0: $i] : ld(iPr_def_10,mult(X0,iPr_def_10)) = mult(mult(X0,iPr_def_10),iPr_def_10),
inference(light_normalisation,[status(thm)],[c_10738,c_9435]) ).
tcf(c_13289,plain,
! [X0: $i] : ld(iPr_def_10,X0) = mult(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_51,c_10827]) ).
tcf(c_13349,plain,
mult(iPr_def_11,iPr_def_10) = sK0,
inference(demodulation,[status(thm)],[c_141,c_13289]) ).
tcf(c_13375,plain,
mult(sK0,iPr_def_10) = mult(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_9466,c_13349]) ).
tcf(c_13377,plain,
mult(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_13375,c_145]) ).
tcf(c_13494,plain,
ld(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_13377,c_50]) ).
tcf(c_14043,plain,
mult(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_13494,c_13289]) ).
tcf(c_14051,plain,
rd(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_14043,c_52]) ).
tcf(c_14069,plain,
sK0 = iPr_def_12,
inference(demodulation,[status(thm)],[c_150,c_14051]) ).
tcf(c_14154,plain,
mult(iPr_def_10,iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_82,c_14069]) ).
tcf(c_14155,plain,
( ( iPr_def_12 != iPr_def_12 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_84,c_14069]) ).
tcf(c_14156,plain,
iPr_def_11 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_14155]) ).
tcf(c_14157,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_13377,c_14154]) ).
tcf(c_14158,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14157,c_14156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:34:03 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 5.89/1.59 % SZS status Started for theBenchmark.p
% 5.89/1.59 % SZS status Theorem for theBenchmark.p
% 5.89/1.59
% 5.89/1.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.89/1.59
% 5.89/1.59 % ------ iProver source info
% 5.89/1.59
% 5.89/1.59 % git: date: 2026-07-19 20:42:38 +0200
% 5.89/1.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.89/1.59 % git: non_committed_changes: false
% 5.89/1.59
% 5.89/1.59 % ------ Parsing...
% 5.89/1.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.89/1.59
% 5.89/1.59 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.89/1.59
% 5.89/1.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.89/1.59
% 5.89/1.59 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 5.89/1.59 % ------ Proving...
% 5.89/1.59 % ------ Problem Properties
% 5.89/1.59
% 5.89/1.59 %
% 5.89/1.59 % clauses 9
% 5.89/1.59 % conjectures 1
% 5.89/1.59 % EPR 1
% 5.89/1.59 % Horn 9
% 5.89/1.59 % unary 8
% 5.89/1.59 % binary 1
% 5.89/1.59 % lits 10
% 5.89/1.59 % lits eq 10
% 5.89/1.59 % fd_pure 0
% 5.89/1.59 % fd_pseudo 0
% 5.89/1.59 % fd_cond 0
% 5.89/1.59 % fd_pseudo_cond 0
% 5.89/1.59 % AC symbols 0
% 5.89/1.59
% 5.89/1.59 % ------ Schedule dynamic 5 is on
% 5.89/1.59
% 5.89/1.59 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 5.89/1.59
% 5.89/1.59
% 5.89/1.59 % ------
% 5.89/1.59 % Current options:
% 5.89/1.59 % ------
% 5.89/1.59
% 5.89/1.59
% 5.89/1.59 %
% 5.89/1.59
% 5.89/1.59 % ------ Proving...
% 5.89/1.59 %
% 5.89/1.59
% 5.89/1.59 % SZS status Theorem for theBenchmark.p
% 5.89/1.59
% 5.89/1.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.89/1.59
% 5.89/1.59
%------------------------------------------------------------------------------