%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 12:53:48 PM UTC 2026
% Result : Theorem 2.42s 16.21s
% Output : CNFRefutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 90 ( 66 unt; 1 def)
% Number of atoms : 191 ( 100 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 38 ~; 32 |; 20 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 80 !; 9 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,conjecture,
! [X0,X1,X2] :
( ( X2 = times(X0,X1)
& element(X1)
& element(X0) )
=> element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(f4,negated_conjecture,
~ ! [X0,X1,X2] :
( ( X2 = times(X0,X1)
& element(X1)
& element(X0) )
=> element(X2) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
? [X0,X1,X2] :
( X2 = times(X0,X1)
& element(X1)
& element(X0)
& ~ element(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1,X2] :
( X2 = times(X0,X1)
& element(X1)
& element(X0)
& ~ element(X2) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ( ~ element(X0)
| ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 ) )
& ( ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 )
| element(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ( ~ element(X0)
| ? [X2] :
( times(X0,X0) = X2
& times(X0,X2) = X0 ) )
& ( ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 )
| element(X0) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
! [X0] :
( ( ~ element(X0)
| ( times(X0,X0) = sK0(X0)
& times(X0,sK0(X0)) = X0 ) )
& ( ! [X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0 )
| element(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f8]) ).
fof(f10,plain,
( sK3 = times(sK1,sK2)
& element(sK2)
& element(sK1)
& ~ element(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f6]) ).
fof(f11,plain,
! [X2,X0,X1] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0] :
( ~ element(X0)
| times(X0,X0) = sK0(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0] :
( ~ element(X0)
| times(X0,sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0
| element(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
sK3 = times(sK1,sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
element(sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
element(sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
~ element(sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X0] :
( times(X0,times(X0,X0)) != X0
| element(X0) ),
inference(equality_resolution,[],[f14]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_50,plain,
! [X0: $i] :
( element(X0)
| ( times(X0,times(X0,X0)) != X0 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,plain,
! [X0: $i] :
( ( times(X0,sK0(X0)) = X0 )
| ~ element(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_52,plain,
! [X0: $i] :
( ( times(X0,X0) = sK0(X0) )
| ~ element(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_53,negated_conjecture,
~ element(sK3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,negated_conjecture,
element(sK1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,negated_conjecture,
element(sK2),
inference(cnf_transformation,[],[f16]) ).
tcf(c_56,negated_conjecture,
times(sK1,sK2) = sK3,
inference(cnf_transformation,[],[f15]) ).
tcf(c_159,definition,
iPr_def_10 = times(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_160,negated_conjecture,
iPr_def_10 = sK3,
inference(demodulation,[status(thm)],[c_56,c_159]) ).
tcf(c_161,negated_conjecture,
element(sK2),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_162,negated_conjecture,
element(sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_164,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( element(X0)
| ~ element(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_265,plain,
times(sK1,sK0(sK1)) = sK1,
inference(superposition,[status(thm)],[c_162,c_51]) ).
tcf(c_266,plain,
times(sK2,sK0(sK2)) = sK2,
inference(superposition,[status(thm)],[c_161,c_51]) ).
tcf(c_268,plain,
! [X0: $i] : times(sK2,times(X0,sK1)) = times(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_159,c_49]) ).
tcf(c_269,plain,
! [X0: $i] : times(sK0(sK1),times(X0,sK1)) = times(sK1,X0),
inference(superposition,[status(thm)],[c_265,c_49]) ).
tcf(c_270,plain,
! [X0: $i] : times(sK0(sK2),times(X0,sK2)) = times(sK2,X0),
inference(superposition,[status(thm)],[c_266,c_49]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
inference(superposition,[status(thm)],[c_49,c_49]) ).
tcf(c_280,plain,
times(sK1,sK1) = sK0(sK1),
inference(superposition,[status(thm)],[c_162,c_52]) ).
tcf(c_281,plain,
times(sK2,sK2) = sK0(sK2),
inference(superposition,[status(thm)],[c_161,c_52]) ).
tcf(c_294,plain,
! [X0: $i] : times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(superposition,[status(thm)],[c_280,c_49]) ).
tcf(c_297,plain,
! [X0: $i] : times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(superposition,[status(thm)],[c_281,c_49]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] : times(sK2,times(X0,times(sK1,X1))) = times(iPr_def_10,times(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_268]) ).
tcf(c_305,plain,
! [X0: $i] :
( element(sK3)
| ~ element(X0)
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ( sK3 = X0 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_166]) ).
tcf(c_319,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ( sK3 != sK3 )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_320,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_164]) ).
tcf(c_327,plain,
times(sK0(sK2),iPr_def_10) = times(sK2,sK1),
inference(superposition,[status(thm)],[c_159,c_270]) ).
tcf(c_339,plain,
( ( sK3 = iPr_def_10 )
| ( iPr_def_10 != sK3 )
| ( sK3 != sK3 ) ),
inference(instantiation,[status(thm)],[c_319]) ).
tcf(c_345,plain,
( element(sK3)
| ~ element(iPr_def_10)
| ( sK3 != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_349,plain,
times(sK0(sK1),sK1) = times(sK1,sK0(sK1)),
inference(superposition,[status(thm)],[c_280,c_294]) ).
tcf(c_352,plain,
times(sK0(sK1),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_349,c_265]) ).
tcf(c_368,plain,
times(iPr_def_10,sK0(sK1)) = times(sK2,sK1),
inference(superposition,[status(thm)],[c_352,c_268]) ).
tcf(c_372,plain,
times(sK0(sK2),sK1) = times(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_159,c_297]) ).
tcf(c_373,plain,
times(sK0(sK2),sK2) = times(sK2,sK0(sK2)),
inference(superposition,[status(thm)],[c_281,c_297]) ).
tcf(c_376,plain,
times(sK0(sK2),sK2) = sK2,
inference(light_normalisation,[status(thm)],[c_373,c_266]) ).
tcf(c_381,plain,
( element(iPr_def_10)
| ( times(iPr_def_10,times(iPr_def_10,iPr_def_10)) != iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
inference(demodulation,[status(thm)],[c_271,c_49]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : times(sK1,times(sK1,times(X0,X1))) = times(X0,times(X1,sK0(sK1))),
inference(superposition,[status(thm)],[c_280,c_406]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] : times(sK2,times(sK2,times(X0,X1))) = times(X0,times(X1,sK0(sK2))),
inference(superposition,[status(thm)],[c_281,c_406]) ).
tcf(c_598,plain,
times(sK0(sK1),sK0(sK2)) = times(sK1,times(sK2,iPr_def_10)),
inference(superposition,[status(thm)],[c_372,c_294]) ).
tcf(c_600,plain,
times(sK2,times(sK2,iPr_def_10)) = times(iPr_def_10,sK0(sK2)),
inference(superposition,[status(thm)],[c_372,c_268]) ).
tcf(c_631,plain,
! [X0: $i] : times(X0,times(sK1,sK0(sK1))) = times(sK1,times(sK0(sK1),X0)),
inference(superposition,[status(thm)],[c_294,c_445]) ).
tcf(c_673,plain,
! [X0: $i] : times(sK1,times(sK0(sK1),X0)) = times(X0,sK1),
inference(light_normalisation,[status(thm)],[c_631,c_265]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,times(sK1,sK0(sK1)))) = times(times(X0,X1),sK1),
inference(superposition,[status(thm)],[c_673,c_406]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i] : times(times(X0,X1),sK1) = times(X0,times(X1,sK1)),
inference(light_normalisation,[status(thm)],[c_785,c_265]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,sK1)) = times(X1,times(sK1,X0)),
inference(demodulation,[status(thm)],[c_789,c_49]) ).
tcf(c_855,plain,
! [X0: $i] : times(sK2,times(X0,sK1)) = times(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_159,c_839]) ).
tcf(c_872,plain,
! [X0: $i] : times(X0,times(sK1,sK2)) = times(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_839,c_268]) ).
tcf(c_874,plain,
! [X0: $i] : times(X0,times(sK1,sK0(sK1))) = times(sK1,X0),
inference(superposition,[status(thm)],[c_839,c_269]) ).
tcf(c_893,plain,
! [X0: $i] : times(X0,iPr_def_10) = times(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_872,c_159]) ).
tcf(c_897,plain,
! [X0: $i] : times(X0,sK1) = times(sK1,X0),
inference(light_normalisation,[status(thm)],[c_874,c_265]) ).
tcf(c_908,plain,
times(iPr_def_10,sK0(sK2)) = times(sK2,sK1),
inference(demodulation,[status(thm)],[c_327,c_893]) ).
tcf(c_910,plain,
times(iPr_def_10,sK0(sK1)) = times(sK1,sK2),
inference(demodulation,[status(thm)],[c_368,c_897]) ).
tcf(c_911,plain,
times(iPr_def_10,sK0(sK1)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_910,c_159]) ).
tcf(c_981,plain,
! [X0: $i,X1: $i] : times(times(sK1,X0),X1) = times(sK1,times(X1,X0)),
inference(superposition,[status(thm)],[c_897,c_49]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i] : times(sK1,times(X0,times(sK2,X1))) = times(iPr_def_10,times(X0,X1)),
inference(demodulation,[status(thm)],[c_300,c_406]) ).
tcf(c_1287,plain,
times(sK1,times(sK2,iPr_def_10)) = times(iPr_def_10,times(sK2,sK1)),
inference(superposition,[status(thm)],[c_855,c_1156]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,sK1)) = times(sK1,times(X1,X0)),
inference(demodulation,[status(thm)],[c_981,c_49]) ).
tcf(c_1428,plain,
! [X0: $i] : times(sK1,times(X0,sK2)) = times(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_855,c_1427]) ).
tcf(c_1429,plain,
! [X0: $i] : times(sK1,times(X0,sK2)) = times(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_268,c_1427]) ).
tcf(c_1834,plain,
times(sK1,times(sK2,iPr_def_10)) = times(iPr_def_10,times(sK1,sK2)),
inference(superposition,[status(thm)],[c_1428,c_1156]) ).
tcf(c_1838,plain,
times(sK1,times(sK2,iPr_def_10)) = times(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1834,c_159,c_1287]) ).
tcf(c_1878,plain,
times(iPr_def_10,sK0(sK2)) = times(sK1,sK2),
inference(superposition,[status(thm)],[c_376,c_1429]) ).
tcf(c_1888,plain,
times(iPr_def_10,sK0(sK2)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1878,c_159,c_908]) ).
tcf(c_2288,plain,
times(iPr_def_10,times(sK0(sK1),sK0(sK2))) = times(sK2,times(sK2,iPr_def_10)),
inference(superposition,[status(thm)],[c_911,c_447]) ).
tcf(c_2324,plain,
times(iPr_def_10,times(iPr_def_10,iPr_def_10)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2288,c_598,c_600,c_1838,c_1888]) ).
tcf(c_2356,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2324,c_381,c_345,c_339,c_320,c_160,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/15.38 % Computer : n003.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Fri Sep 25 05:06:37 UTC 2026
% 0.09/15.39 % CPUTime :
% 0.09/15.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/15.42 Running first-order theorem proving
% 0.16/15.42 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
% 0.16/15.44
% 0.16/15.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/15.44
% 0.16/15.44 % Detected problem language: tptp
% 0.16/15.45 % Proving...
% 2.42/16.21 % SZS status Started for theBenchmark.p
% 2.42/16.21 % SZS status Theorem for theBenchmark.p
% 2.42/16.21
% 2.42/16.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.42/16.21
% 2.42/16.21 % ------ iProver source info
% 2.42/16.21
% 2.42/16.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.42/16.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.42/16.21 % git: non_committed_changes: false
% 2.42/16.21
% 2.42/16.21 % ------ Parsing...
% 2.42/16.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.42/16.21
% 2.42/16.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.42/16.21
% 2.42/16.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.42/16.21
% 2.42/16.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.42/16.21 % ------ Proving...
% 2.42/16.21 % ------ Problem Properties
% 2.42/16.21
% 2.42/16.21 %
% 2.42/16.21 % clauses 9
% 2.42/16.21 % conjectures 4
% 2.42/16.21 % EPR 4
% 2.42/16.21 % Horn 9
% 2.42/16.21 % unary 6
% 2.42/16.21 % binary 3
% 2.42/16.21 % lits 12
% 2.42/16.21 % lits eq 6
% 2.42/16.21 % fd_pure 0
% 2.42/16.21 % fd_pseudo 0
% 2.42/16.21 % fd_cond 0
% 2.42/16.21 % fd_pseudo_cond 0
% 2.42/16.21 % AC symbols 0
% 2.42/16.21
% 2.42/16.21 % ------ Schedule dynamic 5 is on
% 2.42/16.21
% 2.42/16.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.42/16.21
% 2.42/16.21
% 2.42/16.21 % ------
% 2.42/16.21 % Current options:
% 2.42/16.21 % ------
% 2.42/16.21
% 2.42/16.21
% 2.42/16.21 %
% 2.42/16.21
% 2.42/16.21 % ------ Proving...
% 2.42/16.21 %
% 2.42/16.21
% 2.42/16.21 % SZS status Theorem for theBenchmark.p
% 2.42/16.21
% 2.42/16.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.42/16.21
% 2.42/16.21
%------------------------------------------------------------------------------