%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 6.13s 6.77s
% Output : CNFRefutation 6.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 82 ( 65 unt; 1 def)
% Number of atoms : 163 ( 78 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 61 ( 25 ~; 18 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 68 !; 7 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X0) = X1
& times(X0,X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,conjecture,
! [X0,X1] :
( ( element(X1)
& element(X0) )
=> element(times(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f4,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1)
& element(X0) )
=> element(times(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
? [X0,X1] :
( element(X1)
& element(X0)
& ~ element(times(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
( element(X1)
& element(X0)
& ~ element(times(X0,X1)) ),
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,
( element(sK2)
& element(sK1)
& ~ element(times(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[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,
element(sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
element(sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
~ element(times(sK1,sK2)),
inference(cnf_transformation,[],[f10]) ).
fof(f18,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,[],[f18]) ).
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(times(sK1,sK2)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,negated_conjecture,
element(sK1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_55,negated_conjecture,
element(sK2),
inference(cnf_transformation,[],[f15]) ).
tcf(c_156,definition,
iPr_def_10 = times(sK1,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_157,negated_conjecture,
element(sK2),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_158,negated_conjecture,
element(sK1),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_159,negated_conjecture,
~ element(iPr_def_10),
inference(demodulation,[status(thm)],[c_53,c_156]) ).
tcf(c_256,plain,
times(sK1,sK0(sK1)) = sK1,
inference(superposition,[status(thm)],[c_158,c_51]) ).
tcf(c_257,plain,
times(sK2,sK0(sK2)) = sK2,
inference(superposition,[status(thm)],[c_157,c_51]) ).
tcf(c_262,plain,
times(sK1,sK1) = sK0(sK1),
inference(superposition,[status(thm)],[c_158,c_52]) ).
tcf(c_263,plain,
times(sK2,sK2) = sK0(sK2),
inference(superposition,[status(thm)],[c_157,c_52]) ).
tcf(c_265,plain,
! [X0: $i] : times(sK2,times(X0,sK1)) = times(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_156,c_49]) ).
tcf(c_266,plain,
! [X0: $i] : times(sK0(sK1),times(X0,sK1)) = times(sK1,X0),
inference(superposition,[status(thm)],[c_256,c_49]) ).
tcf(c_267,plain,
! [X0: $i] : times(sK0(sK2),times(X0,sK2)) = times(sK2,X0),
inference(superposition,[status(thm)],[c_257,c_49]) ).
tcf(c_268,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_285,plain,
! [X0: $i] : times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(superposition,[status(thm)],[c_262,c_49]) ).
tcf(c_288,plain,
! [X0: $i] : times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(superposition,[status(thm)],[c_263,c_49]) ).
tcf(c_291,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_265]) ).
tcf(c_292,plain,
times(sK2,sK0(sK1)) = times(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_262,c_265]) ).
tcf(c_298,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_323,plain,
times(sK0(sK2),iPr_def_10) = times(sK2,sK1),
inference(superposition,[status(thm)],[c_156,c_267]) ).
tcf(c_342,plain,
times(sK0(sK1),sK1) = times(sK1,sK0(sK1)),
inference(superposition,[status(thm)],[c_262,c_285]) ).
tcf(c_345,plain,
times(sK0(sK1),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_342,c_256]) ).
tcf(c_350,plain,
! [X0: $i] : times(sK1,times(X0,sK0(sK1))) = times(sK1,X0),
inference(superposition,[status(thm)],[c_345,c_49]) ).
tcf(c_353,plain,
times(iPr_def_10,sK0(sK1)) = times(sK2,sK1),
inference(superposition,[status(thm)],[c_345,c_265]) ).
tcf(c_359,plain,
times(sK0(sK2),sK1) = times(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_156,c_288]) ).
tcf(c_360,plain,
times(sK0(sK2),sK2) = times(sK2,sK0(sK2)),
inference(superposition,[status(thm)],[c_263,c_288]) ).
tcf(c_363,plain,
times(sK0(sK2),sK2) = sK2,
inference(light_normalisation,[status(thm)],[c_360,c_257]) ).
tcf(c_400,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_268,c_49]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : times(sK1,times(sK1,times(X0,X1))) = times(X0,times(X1,sK0(sK1))),
inference(superposition,[status(thm)],[c_262,c_400]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i] : times(sK2,times(sK2,times(X0,X1))) = times(X0,times(X1,sK0(sK2))),
inference(superposition,[status(thm)],[c_263,c_400]) ).
tcf(c_588,plain,
times(sK0(sK1),sK0(sK2)) = times(sK1,times(sK2,iPr_def_10)),
inference(superposition,[status(thm)],[c_359,c_285]) ).
tcf(c_590,plain,
times(sK2,times(sK2,iPr_def_10)) = times(iPr_def_10,sK0(sK2)),
inference(superposition,[status(thm)],[c_359,c_265]) ).
tcf(c_604,plain,
times(sK1,times(iPr_def_10,sK1)) = times(sK1,sK2),
inference(superposition,[status(thm)],[c_292,c_350]) ).
tcf(c_611,plain,
times(sK1,times(iPr_def_10,sK1)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_604,c_156]) ).
tcf(c_641,plain,
times(sK0(sK1),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_611,c_285]) ).
tcf(c_659,plain,
! [X0: $i] : times(X0,times(sK1,sK0(sK1))) = times(sK1,times(sK0(sK1),X0)),
inference(superposition,[status(thm)],[c_285,c_439]) ).
tcf(c_703,plain,
! [X0: $i] : times(sK1,times(sK0(sK1),X0)) = times(X0,sK1),
inference(light_normalisation,[status(thm)],[c_659,c_256]) ).
tcf(c_830,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,times(sK1,sK0(sK1)))) = times(times(X0,X1),sK1),
inference(superposition,[status(thm)],[c_703,c_400]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i] : times(times(X0,X1),sK1) = times(X0,times(X1,sK1)),
inference(light_normalisation,[status(thm)],[c_830,c_256]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,sK1)) = times(X1,times(sK1,X0)),
inference(demodulation,[status(thm)],[c_834,c_49]) ).
tcf(c_883,plain,
! [X0: $i] : times(sK2,times(X0,sK1)) = times(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_156,c_867]) ).
tcf(c_900,plain,
! [X0: $i] : times(X0,times(sK1,sK2)) = times(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_867,c_265]) ).
tcf(c_902,plain,
! [X0: $i] : times(X0,times(sK1,sK0(sK1))) = times(sK1,X0),
inference(superposition,[status(thm)],[c_867,c_266]) ).
tcf(c_921,plain,
! [X0: $i] : times(X0,iPr_def_10) = times(iPr_def_10,X0),
inference(light_normalisation,[status(thm)],[c_900,c_156]) ).
tcf(c_925,plain,
! [X0: $i] : times(X0,sK1) = times(sK1,X0),
inference(light_normalisation,[status(thm)],[c_902,c_256]) ).
tcf(c_936,plain,
times(iPr_def_10,sK0(sK1)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_641,c_921]) ).
tcf(c_937,plain,
times(iPr_def_10,sK0(sK2)) = times(sK2,sK1),
inference(demodulation,[status(thm)],[c_323,c_921]) ).
tcf(c_938,plain,
times(sK2,sK1) = iPr_def_10,
inference(demodulation,[status(thm)],[c_353,c_936]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] : times(times(sK1,X0),X1) = times(sK1,times(X1,X0)),
inference(superposition,[status(thm)],[c_925,c_49]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i] : times(sK1,times(X0,times(sK2,X1))) = times(iPr_def_10,times(X0,X1)),
inference(demodulation,[status(thm)],[c_291,c_400]) ).
tcf(c_1257,plain,
times(sK1,times(sK2,iPr_def_10)) = times(iPr_def_10,times(sK2,sK1)),
inference(superposition,[status(thm)],[c_883,c_1131]) ).
tcf(c_1261,plain,
times(sK1,times(sK2,iPr_def_10)) = times(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1257,c_938]) ).
tcf(c_1942,plain,
! [X0: $i,X1: $i] : times(X0,times(X1,sK1)) = times(sK1,times(X1,X0)),
inference(demodulation,[status(thm)],[c_1012,c_49]) ).
tcf(c_1944,plain,
! [X0: $i] : times(sK1,times(X0,sK2)) = times(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_265,c_1942]) ).
tcf(c_2071,plain,
times(iPr_def_10,sK0(sK2)) = times(sK1,sK2),
inference(superposition,[status(thm)],[c_363,c_1944]) ).
tcf(c_2081,plain,
times(iPr_def_10,sK0(sK2)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2071,c_156,c_937]) ).
tcf(c_2437,plain,
times(iPr_def_10,times(sK0(sK1),sK0(sK2))) = times(sK2,times(sK2,iPr_def_10)),
inference(superposition,[status(thm)],[c_936,c_441]) ).
tcf(c_2472,plain,
times(iPr_def_10,times(iPr_def_10,iPr_def_10)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2437,c_588,c_590,c_1261,c_2081]) ).
tcf(c_2499,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2472,c_298,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.39 % Computer : n014.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Fri Sep 25 05:04:24 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.46 Running first-order theorem proving
% 0.17/5.46 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
% 0.17/5.47
% 0.17/5.47 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.47
% 0.17/5.48 % Detected problem language: tptp
% 0.17/5.50 % Proving...
% 6.13/6.77 % SZS status Started for theBenchmark.p
% 6.13/6.77 % SZS status Theorem for theBenchmark.p
% 6.13/6.77
% 6.13/6.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.13/6.77
% 6.13/6.77 % ------ iProver source info
% 6.13/6.77
% 6.13/6.77 % git: date: 2026-07-19 20:42:38 +0200
% 6.13/6.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.13/6.77 % git: non_committed_changes: false
% 6.13/6.77
% 6.13/6.77 % ------ Parsing...
% 6.13/6.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.13/6.77
% 6.13/6.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.13/6.77
% 6.13/6.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.13/6.77
% 6.13/6.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.13/6.77 % ------ Proving...
% 6.13/6.77 % ------ Problem Properties
% 6.13/6.77
% 6.13/6.77 %
% 6.13/6.77 % clauses 8
% 6.13/6.77 % conjectures 3
% 6.13/6.77 % EPR 3
% 6.13/6.77 % Horn 8
% 6.13/6.77 % unary 5
% 6.13/6.77 % binary 3
% 6.13/6.77 % lits 11
% 6.13/6.77 % lits eq 5
% 6.13/6.77 % fd_pure 0
% 6.13/6.77 % fd_pseudo 0
% 6.13/6.77 % fd_cond 0
% 6.13/6.77 % fd_pseudo_cond 0
% 6.13/6.77 % AC symbols 0
% 6.13/6.77
% 6.13/6.77 % ------ Schedule dynamic 5 is on
% 6.13/6.77
% 6.13/6.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.13/6.77
% 6.13/6.77
% 6.13/6.77 % ------
% 6.13/6.77 % Current options:
% 6.13/6.77 % ------
% 6.13/6.77
% 6.13/6.77
% 6.13/6.77 %
% 6.13/6.77
% 6.13/6.77 % ------ Proving...
% 6.13/6.77 %
% 6.13/6.77
% 6.13/6.77 % SZS status Theorem for theBenchmark.p
% 6.13/6.77
% 6.13/6.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.13/6.77
% 6.13/6.77
%------------------------------------------------------------------------------