%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM149+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 01:04:30 PM UTC 2026
% Result : Theorem 1.35s 1.74s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 20 unt; 2 def)
% Number of atoms : 192 ( 89 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 152 ( 50 ~; 51 |; 43 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 163 ( 0 sgn 111 !; 52 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( X3 = vabs(X0,X1,X2)
=> visValue(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isValue0) ).
fof(f8,axiom,
! [X0,X1] :
( X1 = vvar(X0)
=> ~ visValue(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isValue1) ).
fof(f18,axiom,
! [X0] : vnoType != vsomeType(X0),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','DIFF-noType-someType') ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( ( X2 = vempty
& X1 = X0 )
=> ( X3 = vlookup(X1,X2)
=> X3 = vnoType ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',lookup0) ).
fof(f54,axiom,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X7,X4,X8] :
( vtcheck(X2,X4,X8)
& vtcheck(X2,X7,varrow(X8,X1))
& X0 = vapp(X7,X4) )
| ? [X3,X4,X5,X6] :
( vtcheck(vbind(X3,X5,X2),X4,X6)
& X1 = varrow(X5,X6)
& X0 = vabs(X3,X5,X4) )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','T-inv') ).
fof(f57,conjecture,
! [X0,X1] :
( ( ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) )
=> ? [X2] : vreduce(vvar(X1)) = vsomeExp(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Progress-T-var') ).
fof(f58,negated_conjecture,
~ ! [X0,X1] :
( ( ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) )
=> ? [X2] : vreduce(vvar(X1)) = vsomeExp(X2) ),
inference(negated_conjecture,[status(cth)],[f57]) ).
fof(f65,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ) ),
inference(rectify,[],[f54]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f72,plain,
! [X0,X1] :
( vvar(X0) != X1
| ~ visValue(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( vempty != X2
| X0 != X1
| vlookup(X1,X2) != X3
| X3 = vnoType ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( vempty != X2
| X0 != X1
| vlookup(X1,X2) != X3
| X3 = vnoType ),
inference(flattening,[],[f87]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 )
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(flattening,[],[f141]) ).
fof(f147,plain,
? [X0,X1] :
( ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0)
& ! [X2] : vsomeExp(X2) != vreduce(vvar(X1)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f148,plain,
? [X0,X1] :
( ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0)
& ! [X2] : vsomeExp(X2) != vreduce(vvar(X1)) ),
inference(flattening,[],[f147]) ).
fof(f210,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| ( vtcheck(vbind(sK83(X0,X1,X2),sK85(X0,X1,X2),X2),sK84(X0,X1,X2),sK86(X0,X1,X2))
& varrow(sK85(X0,X1,X2),sK86(X0,X1,X2)) = X1
& vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0 )
| ( vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2)
& vvar(sK82(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82,sK83,sK84,sK85,sK86]),skolemize(X3,sK82(X0,X1,X2)),skolemize(X4,sK83(X0,X1,X2)),skolemize(X5,sK84(X0,X1,X2)),skolemize(X6,sK85(X0,X1,X2)),skolemize(X7,sK86(X0,X1,X2))],[f165]) ).
fof(f211,plain,
( ~ visValue(vvar(sK88))
& vtcheck(vempty,vvar(sK88),sK87)
& ! [X2] : vsomeExp(X2) != vreduce(vvar(sK88)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88]),skolemize(X0,sK87),skolemize(X1,sK88)],[f148]) ).
fof(f222,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f5]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( vabs(X0,X1,X2) != X3
| visValue(X3) ),
inference(cnf_transformation,[],[f71]) ).
fof(f225,plain,
! [X0,X1] :
( vvar(X0) != X1
| ~ visValue(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f244,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f18]) ).
fof(f248,plain,
! [X2,X3,X0,X1] :
( vempty != X2
| X0 != X1
| vlookup(X1,X2) != X3
| vnoType = X3 ),
inference(cnf_transformation,[],[f88]) ).
fof(f356,plain,
! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| vabs(sK83(X0,X1,X2),sK85(X0,X1,X2),sK84(X0,X1,X2)) = X0
| vsomeType(X1) = vlookup(sK82(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f210]) ).
fof(f363,plain,
vtcheck(vempty,vvar(sK88),sK87),
inference(cnf_transformation,[],[f211]) ).
fof(f371,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f224]) ).
fof(f372,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f225]) ).
fof(f400,plain,
! [X2,X0,X1] :
( vempty != X2
| X0 != X1
| vnoType = vlookup(X1,X2) ),
inference(equality_resolution,[],[f248]) ).
fof(f401,plain,
! [X2,X1] :
( vempty != X2
| vnoType = vlookup(X1,X2) ),
inference(equality_resolution,[],[f400]) ).
fof(f402,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f401]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : vapp(X0,X1) != vvar(X2),
inference(cnf_transformation,[],[f222]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : visValue(vabs(X0,X1,X2)),
inference(cnf_transformation,[],[f371]) ).
tcf(c_59,plain,
! [X0: $i] : ~ visValue(vvar(X0)),
inference(cnf_transformation,[],[f372]) ).
tcf(c_74,plain,
! [X0: $i] : vsomeType(X0) != vnoType,
inference(cnf_transformation,[],[f244]) ).
tcf(c_78,plain,
! [X0: $i] : vlookup(X0,vempty) = vnoType,
inference(cnf_transformation,[],[f402]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP12(X1,X2,X0)
| ( vlookup(sK82(X1,X2,X0),X0) = vsomeType(X2) )
| ( vabs(sK83(X1,X2,X0),sK85(X1,X2,X0),sK84(X1,X2,X0)) = X1 )
| ~ vtcheck(X0,X1,X2) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_190,negated_conjecture,
vtcheck(vempty,vvar(sK88),sK87),
inference(cnf_transformation,[],[f363]) ).
tcf(c_13192,definition,
iPr_def_10 = vvar(sK88),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13193,negated_conjecture,
vtcheck(vempty,iPr_def_10,sK87),
inference(demodulation,[status(thm)],[c_190,c_13192]) ).
tcf(c_16195,plain,
~ visValue(iPr_def_10),
inference(superposition,[status(thm)],[c_13192,c_59]) ).
tcf(c_26219,plain,
( sP12(iPr_def_10,sK87,vempty)
| ( vlookup(sK82(iPr_def_10,sK87,vempty),vempty) = vsomeType(sK87) )
| ( vabs(sK83(iPr_def_10,sK87,vempty),sK85(iPr_def_10,sK87,vempty),sK84(iPr_def_10,sK87,vempty)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13193,c_184]) ).
tcf(c_26542,plain,
( sP12(iPr_def_10,sK87,vempty)
| ( vsomeType(sK87) = vnoType )
| ( vabs(sK83(iPr_def_10,sK87,vempty),sK85(iPr_def_10,sK87,vempty),sK84(iPr_def_10,sK87,vempty)) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_26219,c_78]) ).
tcf(c_26543,plain,
( sP12(iPr_def_10,sK87,vempty)
| ( vabs(sK83(iPr_def_10,sK87,vempty),sK85(iPr_def_10,sK87,vempty),sK84(iPr_def_10,sK87,vempty)) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26542,c_74]) ).
fof(f164,definition,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 ) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ vtcheck(X2,X0,X1)
| sP12(X0,X1,X2)
| ? [X4,X5,X6,X7] :
( vtcheck(vbind(X4,X6,X2),X5,X7)
& varrow(X6,X7) = X1
& vabs(X4,X6,X5) = X0 )
| ? [X3] :
( vlookup(X3,X2) = vsomeType(X1)
& X0 = vvar(X3) ) ),
inference(definition_folding,[],[f142,f164]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X8,X9,X10] :
( vtcheck(X2,X9,X10)
& vtcheck(X2,X8,varrow(X10,X1))
& vapp(X8,X9) = X0 ) ),
inference(nnf_transformation,[],[f164]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 ) ),
inference(rectify,[],[f207]) ).
fof(f209,plain,
! [X0,X1,X2] :
( ~ sP12(X0,X1,X2)
| ( vtcheck(X2,sK80(X0,X1,X2),sK81(X0,X1,X2))
& vtcheck(X2,sK79(X0,X1,X2),varrow(sK81(X0,X1,X2),X1))
& vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79,sK80,sK81]),skolemize(X3,sK79(X0,X1,X2)),skolemize(X4,sK80(X0,X1,X2)),skolemize(X5,sK81(X0,X1,X2))],[f208]) ).
fof(f353,plain,
! [X2,X0,X1] :
( ~ sP12(X0,X1,X2)
| vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( vapp(sK79(X0,X1,X2),sK80(X0,X1,X2)) = X0 )
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_26550,plain,
( ( vapp(sK79(iPr_def_10,sK87,vempty),sK80(iPr_def_10,sK87,vempty)) = iPr_def_10 )
| ( vabs(sK83(iPr_def_10,sK87,vempty),sK85(iPr_def_10,sK87,vempty),sK84(iPr_def_10,sK87,vempty)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_26543,c_178]) ).
tcf(c_26579,plain,
( visValue(iPr_def_10)
| ( vapp(sK79(iPr_def_10,sK87,vempty),sK80(iPr_def_10,sK87,vempty)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_26550,c_58]) ).
tcf(c_26603,plain,
vapp(sK79(iPr_def_10,sK87,vempty),sK80(iPr_def_10,sK87,vempty)) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_26579,c_16195]) ).
tcf(c_26624,plain,
! [X0: $i] : vvar(X0) != iPr_def_10,
inference(superposition,[status(thm)],[c_26603,c_56]) ).
tcf(c_27747,plain,
$false,
inference(superposition,[status(thm)],[c_13192,c_26624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM149+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:57:52 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 1.35/1.74 % SZS status Started for theBenchmark.p
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74
% 1.35/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.35/1.74
% 1.35/1.74 % ------ iProver source info
% 1.35/1.74
% 1.35/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.35/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.35/1.74 % git: non_committed_changes: false
% 1.35/1.74
% 1.35/1.74 % ------ Parsing...
% 1.35/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.35/1.74
% 1.35/1.74 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.35/1.74
% 1.35/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.35/1.74
% 1.35/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.35/1.74 % ------ Proving...
% 1.35/1.74 % ------ Problem Properties
% 1.35/1.74
% 1.35/1.74 %
% 1.35/1.74 % clauses 138
% 1.35/1.74 % conjectures 1
% 1.35/1.74 % EPR 4
% 1.35/1.74 % Horn 111
% 1.35/1.74 % unary 25
% 1.35/1.74 % binary 86
% 1.35/1.74 % lits 301
% 1.35/1.74 % lits eq 134
% 1.35/1.74 % fd_pure 0
% 1.35/1.74 % fd_pseudo 0
% 1.35/1.74 % fd_cond 3
% 1.35/1.74 % fd_pseudo_cond 20
% 1.35/1.74 % AC symbols 0
% 1.35/1.74
% 1.35/1.74 % ------ Schedule dynamic 5 is on
% 1.35/1.74
% 1.35/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.35/1.74
% 1.35/1.74
% 1.35/1.74 % ------
% 1.35/1.74 % Current options:
% 1.35/1.74 % ------
% 1.35/1.74
% 1.35/1.74
% 1.35/1.74 %
% 1.35/1.74
% 1.35/1.74 % ------ Proving...
% 1.35/1.74 %
% 1.35/1.74
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74
% 1.35/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.35/1.74
% 1.35/1.74
%------------------------------------------------------------------------------