%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO497+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:21:10 PM UTC 2026
% Result : Theorem 7.15s 1.78s
% Output : CNFRefutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 29 unt; 3 def)
% Number of atoms : 172 ( 58 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 151 ( 72 ~; 62 |; 17 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 143 ( 0 sgn 135 !; 8 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( s_e(X1,ext(X0,X1,X2,X3),X2,X3)
& s_t(X0,X1,ext(X0,X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO011+0.ax',aA4) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( s_e(X2,X3,X0,X1)
| ~ s_e(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_2) ).
fof(f12,axiom,
! [X0,X1,X2,X3] :
( s_e(X1,X0,X2,X3)
| ~ s_e(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_4) ).
fof(f17,axiom,
! [X0,X1,X2] :
( X0 = X1
| ~ s_e(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz2_13) ).
fof(f21,axiom,
! [X0,X1,X2] :
( s_t(X2,X1,X0)
| ~ s_t(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_2) ).
fof(f34,axiom,
! [X0,X1] : X0 != ext(X1,X0,alpha,gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14b) ).
fof(f71,axiom,
! [X0,X1,X2,X3] :
( ~ s_t(X2,X1,X3)
| ~ s_t(X0,X1,X3)
| X3 = X1
| X2 = X1
| X0 = X1
| sameside(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3b) ).
fof(f75,axiom,
! [X0,X1,X2] :
( sameside(X2,X1,X0)
| ~ sameside(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_6) ).
fof(f77,conjecture,
! [X0,X1,X2,X3] :
( ( s_e(X1,insert(X2,X3,X1,X0),X2,X3)
| X2 = X3
| X0 = X1 )
& ( sameside(insert(X2,X3,X1,X0),X1,X0)
| X2 = X3
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_11a) ).
fof(f78,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( s_e(X1,insert(X2,X3,X1,X0),X2,X3)
| X2 = X3
| X0 = X1 )
& ( sameside(insert(X2,X3,X1,X0),X1,X0)
| X2 = X3
| X0 = X1 ) ),
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,axiom,
! [X0,X1,X2,X3] : insert(X0,X1,X2,X3) = ext(ext(X3,X2,alpha,gamma),X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_insert) ).
fof(f87,plain,
? [X0,X1,X2,X3] :
( ( ~ s_e(X1,insert(X2,X3,X1,X0),X2,X3)
& X2 != X3
& X0 != X1 )
| ( ~ sameside(insert(X2,X3,X1,X0),X1,X0)
& X2 != X3
& X0 != X1 ) ),
inference(ennf_transformation,[],[f78]) ).
fof(f92,plain,
( sP0(sK2,sK1,sK4,sK3)
| ( ~ sameside(insert(sK3,sK4,sK2,sK1),sK2,sK1)
& sK3 != sK4
& sK1 != sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f89]) ).
fof(f96,plain,
! [X2,X3,X0,X1] : s_e(X1,ext(X0,X1,X2,X3),X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f97,plain,
! [X2,X3,X0,X1] : s_t(X0,X1,ext(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f4]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( s_e(X2,X3,X0,X1)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( s_e(X1,X0,X2,X3)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f113,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ s_e(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f117,plain,
! [X2,X0,X1] :
( s_t(X2,X1,X0)
| ~ s_t(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f130,plain,
! [X0,X1] : ext(X1,X0,alpha,gamma) != X0,
inference(cnf_transformation,[],[f34]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( ~ s_t(X2,X1,X3)
| ~ s_t(X0,X1,X3)
| X1 = X3
| X1 = X2
| X0 = X1
| sameside(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sameside(X2,X1,X0)
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
fof(f185,plain,
( sP0(sK2,sK1,sK4,sK3)
| ~ sameside(insert(sK3,sK4,sK2,sK1),sK2,sK1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f186,plain,
( sP0(sK2,sK1,sK4,sK3)
| sK3 != sK4 ),
inference(cnf_transformation,[],[f92]) ).
fof(f187,plain,
( sP0(sK2,sK1,sK4,sK3)
| sK1 != sK2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f188,plain,
! [X2,X3,X0,X1] : insert(X0,X1,X2,X3) = ext(ext(X3,X2,alpha,gamma),X2,X0,X1),
inference(cnf_transformation,[],[f79]) ).
fof(f228,plain,
( sP0(sK2,sK1,sK4,sK3)
| ~ sameside(ext(ext(sK1,sK2,alpha,gamma),sK2,sK3,sK4),sK2,sK1) ),
inference(definition_unfolding,[],[f185,f188]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : s_t(X0,X1,ext(X0,X1,X2,X3)),
inference(cnf_transformation,[],[f97]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : s_e(X0,ext(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[],[f96]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s_e(X2,X3,X0,X1)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s_e(X1,X0,X2,X3)
| ~ s_e(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ s_e(X0,X1,X2,X2) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( s_t(X2,X1,X0)
| ~ s_t(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : ext(X0,X1,alpha,gamma) != X1,
inference(cnf_transformation,[],[f130]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sameside(X0,X1,X3)
| ( X1 = X3 )
| ( X1 = X2 )
| ( X0 = X1 )
| ~ s_t(X3,X1,X2)
| ~ s_t(X0,X1,X2) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( sameside(X2,X1,X0)
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_141,negated_conjecture,
( sP0(sK2,sK1,sK4,sK3)
| ( sK1 != sK2 ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_142,negated_conjecture,
( sP0(sK2,sK1,sK4,sK3)
| ( sK4 != sK3 ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_143,negated_conjecture,
( sP0(sK2,sK1,sK4,sK3)
| ~ sameside(ext(ext(sK1,sK2,alpha,gamma),sK2,sK3,sK4),sK2,sK1) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_3104,definition,
iPr_def_10 = ext(sK1,sK2,alpha,gamma),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3105,definition,
iPr_def_11 = ext(iPr_def_10,sK2,sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4338,plain,
s_t(sK1,sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_3104,c_52]) ).
tcf(c_4343,plain,
s_t(iPr_def_10,sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_3105,c_52]) ).
tcf(c_4344,plain,
sK2 != iPr_def_10,
inference(superposition,[status(thm)],[c_3104,c_86]) ).
tcf(c_4346,plain,
s_e(sK2,iPr_def_11,sK3,sK4),
inference(superposition,[status(thm)],[c_3105,c_53]) ).
tcf(c_4368,plain,
s_t(iPr_def_11,sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_4343,c_73]) ).
tcf(c_4656,plain,
s_e(sK3,sK4,sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_4346,c_62]) ).
tcf(c_4675,plain,
s_e(sK4,sK3,sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_4656,c_64]) ).
tcf(c_13755,plain,
! [X0: $i] :
( sameside(sK1,sK2,X0)
| ( sK2 = iPr_def_10 )
| ( sK1 = sK2 )
| ( X0 = sK2 )
| ~ s_t(X0,sK2,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4338,c_131]) ).
fof(f88,definition,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ~ s_e(X1,insert(X2,X3,X1,X0),X2,X3)
& X2 != X3
& X0 != X1 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f89,plain,
? [X0,X1,X2,X3] :
( sP0(X1,X0,X3,X2)
| ( ~ sameside(insert(X2,X3,X1,X0),X1,X0)
& X2 != X3
& X0 != X1 ) ),
inference(definition_folding,[],[f87,f88]) ).
fof(f90,plain,
! [X1,X0,X3,X2] :
( ~ sP0(X1,X0,X3,X2)
| ( ~ s_e(X1,insert(X2,X3,X1,X0),X2,X3)
& X2 != X3
& X0 != X1 ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ~ s_e(X0,insert(X3,X2,X0,X1),X3,X2)
& X2 != X3
& X0 != X1 ) ),
inference(rectify,[],[f90]) ).
fof(f182,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ~ s_e(X0,insert(X3,X2,X0,X1),X3,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ~ s_e(X0,ext(ext(X1,X0,alpha,gamma),X0,X3,X2),X3,X2) ),
inference(definition_unfolding,[],[f182,f188]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sP0(X0,X1,X3,X2)
| ~ s_e(X0,ext(ext(X1,X0,alpha,gamma),X0,X2,X3),X2,X3) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ sP0(X0,X1,X2,X3),
inference(backward_subsumption_resolution,[status(thm)],[c_140,c_53]) ).
tcf(c_256,plain,
sK1 != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_141,c_253]) ).
tcf(c_257,plain,
sK4 != sK3,
inference(backward_subsumption_resolution,[status(thm)],[c_142,c_253]) ).
tcf(c_258,plain,
~ sameside(ext(ext(sK1,sK2,alpha,gamma),sK2,sK3,sK4),sK2,sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_143,c_253]) ).
tcf(c_3106,plain,
~ sameside(iPr_def_11,sK2,sK1),
inference(demodulation,[status(thm)],[c_258,c_3104,c_3105]) ).
tcf(c_3107,plain,
sK4 != sK3,
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_3108,plain,
sK1 != sK2,
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_13801,plain,
! [X0: $i] :
( sameside(sK1,sK2,X0)
| ( X0 = sK2 )
| ~ s_t(X0,sK2,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13755,c_4344,c_3108]) ).
tcf(c_14352,plain,
( sameside(sK1,sK2,iPr_def_11)
| ( sK2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4368,c_13801]) ).
tcf(c_16353,plain,
( sameside(iPr_def_11,sK2,sK1)
| ( sK2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_14352,c_136]) ).
tcf(c_16358,plain,
sK2 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_16353,c_3106]) ).
tcf(c_16480,plain,
s_e(sK4,sK3,iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_4675,c_16358]) ).
tcf(c_17060,plain,
sK4 = sK3,
inference(superposition,[status(thm)],[c_16480,c_69]) ).
tcf(c_17061,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_17060,c_3107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO497+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.42 % Computer : n005.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Wed Sep 23 12:13:02 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 0.18/0.47
% 0.18/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.47
% 0.18/0.47 % Detected problem language: tptp
% 0.18/0.48 % Proving...
% 7.15/1.78 % SZS status Started for theBenchmark.p
% 7.15/1.78 % SZS status Theorem for theBenchmark.p
% 7.15/1.78
% 7.15/1.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.15/1.78
% 7.15/1.78 % ------ iProver source info
% 7.15/1.78
% 7.15/1.78 % git: date: 2026-07-19 20:42:38 +0200
% 7.15/1.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.15/1.78 % git: non_committed_changes: false
% 7.15/1.78
% 7.15/1.78 % ------ Parsing...
% 7.15/1.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.15/1.78
% 7.15/1.78 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.15/1.78
% 7.15/1.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.15/1.78
% 7.15/1.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.15/1.78 % ------ Proving...
% 7.15/1.78 % ------ Problem Properties
% 7.15/1.78
% 7.15/1.78 %
% 7.15/1.78 % clauses 105
% 7.15/1.78 % conjectures 0
% 7.15/1.78 % EPR 84
% 7.15/1.78 % Horn 86
% 7.15/1.78 % unary 25
% 7.15/1.78 % binary 33
% 7.15/1.78 % lits 277
% 7.15/1.78 % lits eq 37
% 7.15/1.78 % fd_pure 0
% 7.15/1.78 % fd_pseudo 0
% 7.15/1.78 % fd_cond 0
% 7.15/1.78 % fd_pseudo_cond 19
% 7.15/1.78 % AC symbols 0
% 7.15/1.78
% 7.15/1.78 % ------ Schedule dynamic 5 is on
% 7.15/1.78
% 7.15/1.78 % ------ no conjectures: strip conj schedule
% 7.15/1.78
% 7.15/1.78 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 7.15/1.78
% 7.15/1.78
% 7.15/1.78 % ------
% 7.15/1.78 % Current options:
% 7.15/1.78 % ------
% 7.15/1.78
% 7.15/1.78
% 7.15/1.78 %
% 7.15/1.78
% 7.15/1.78 % ------ Proving...
% 7.15/1.78 %
% 7.15/1.78
% 7.15/1.78 % SZS status Theorem for theBenchmark.p
% 7.15/1.78
% 7.15/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.15/1.79
% 7.15/1.79
%------------------------------------------------------------------------------