%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM130+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 : n008.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 01:04:28 PM UTC 2026
% Result : Theorem 3.33s 1.28s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 13 unt; 0 def)
% Number of atoms : 121 ( 64 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 144 ( 61 ~; 50 |; 24 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 166 ( 0 sgn 150 !; 16 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( X2 = vabs(X3,X0,X5)
& X1 = X4 )
=> ( ( visFreeVar(X1,X2)
=> ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ( visFreeVar(X4,X5)
& X3 != X4 )
=> visFreeVar(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).
fof(f32,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( X4 = vabs(X6,X7,X8)
& X3 = X0
& X2 = X1 )
=> ( X1 = X6
=> ( X5 = vsubst(X2,X3,X4)
=> X5 = vabs(X6,X7,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst3) ).
fof(f56,axiom,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(vbind(X0,X1,X2),X3,X4)
& ~ visFreeVar(X0,X3) )
=> vtcheck(X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong') ).
fof(f59,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
& vtcheck(X1,X3,X0)
& X2 = X4 )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-1') ).
fof(f60,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
& vtcheck(X1,X3,X0)
& X2 = X4 )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f61,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
& vtcheck(X1,X3,X0)
& X2 = X4
& ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
inference(ennf_transformation,[],[f60]) ).
fof(f62,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
& vtcheck(X1,X3,X0)
& X2 = X4
& ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3)
| vtcheck(X2,X3,X4) ),
inference(ennf_transformation,[],[f56]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3)
| vtcheck(X2,X3,X4) ),
inference(flattening,[],[f67]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2
| X1 != X6
| vsubst(X2,X3,X4) != X5
| X5 = vabs(X6,X7,X8) ),
inference(ennf_transformation,[],[f32]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2
| X1 != X6
| vsubst(X2,X3,X4) != X5
| X5 = vabs(X6,X7,X8) ),
inference(flattening,[],[f77]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4,X5] :
( vabs(X3,X0,X5) != X2
| X1 != X4
| ( ( ~ visFreeVar(X1,X2)
| ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ~ visFreeVar(X4,X5)
| X3 = X4
| visFreeVar(X1,X2) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5] :
( vabs(X3,X0,X5) != X2
| X1 != X4
| ( ( ~ visFreeVar(X1,X2)
| ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ~ visFreeVar(X4,X5)
| X3 = X4
| visFreeVar(X1,X2) ) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
( vtcheck(vbind(sK2,sK0,sK1),vabs(sK4,sK5,sK6),sK7)
& vtcheck(sK1,sK3,sK0)
& sK2 = sK4
& ~ vtcheck(sK1,vsubst(sK2,sK3,vabs(sK4,sK5,sK6)),sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f62]) ).
fof(f95,plain,
vtcheck(vbind(sK2,sK0,sK1),vabs(sK4,sK5,sK6),sK7),
inference(cnf_transformation,[],[f94]) ).
fof(f97,plain,
sK2 = sK4,
inference(cnf_transformation,[],[f94]) ).
fof(f98,plain,
~ vtcheck(sK1,vsubst(sK2,sK3,vabs(sK4,sK5,sK6)),sK7),
inference(cnf_transformation,[],[f94]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3)
| vtcheck(X2,X3,X4) ),
inference(cnf_transformation,[],[f68]) ).
fof(f114,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2
| X1 != X6
| vsubst(X2,X3,X4) != X5
| vabs(X6,X7,X8) = X5 ),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4,X5] :
( vabs(X3,X0,X5) != X2
| X1 != X4
| ~ visFreeVar(X1,X2)
| X3 != X4 ),
inference(cnf_transformation,[],[f93]) ).
fof(f132,plain,
~ vtcheck(sK1,vsubst(sK4,sK3,vabs(sK4,sK5,sK6)),sK7),
inference(definition_unfolding,[],[f98,f97]) ).
fof(f133,plain,
vtcheck(vbind(sK4,sK0,sK1),vabs(sK4,sK5,sK6),sK7),
inference(definition_unfolding,[],[f95,f97]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2
| X1 != X6
| vsubst(X2,X3,X4) = vabs(X6,X7,X8) ),
inference(equality_resolution,[],[f114]) ).
fof(f146,plain,
! [X2,X3,X0,X8,X6,X7,X4] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| X2 != X6
| vsubst(X2,X3,X4) = vabs(X6,X7,X8) ),
inference(equality_resolution,[],[f145]) ).
fof(f147,plain,
! [X3,X0,X8,X6,X7,X4] :
( vabs(X6,X7,X8) != X4
| X0 != X3
| vabs(X6,X7,X8) = vsubst(X6,X3,X4) ),
inference(equality_resolution,[],[f146]) ).
fof(f148,plain,
! [X3,X8,X6,X7,X4] :
( vabs(X6,X7,X8) != X4
| vabs(X6,X7,X8) = vsubst(X6,X3,X4) ),
inference(equality_resolution,[],[f147]) ).
fof(f149,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f148]) ).
fof(f179,plain,
! [X2,X0,X1,X4,X5] :
( vabs(X4,X0,X5) != X2
| X1 != X4
| ~ visFreeVar(X1,X2) ),
inference(equality_resolution,[],[f130]) ).
fof(f180,plain,
! [X2,X0,X4,X5] :
( vabs(X4,X0,X5) != X2
| ~ visFreeVar(X4,X2) ),
inference(equality_resolution,[],[f179]) ).
fof(f181,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f180]) ).
tcf(c_49,negated_conjecture,
~ vtcheck(sK1,vsubst(sK4,sK3,vabs(sK4,sK5,sK6)),sK7),
inference(cnf_transformation,[],[f132]) ).
tcf(c_51,negated_conjecture,
vtcheck(vbind(sK4,sK0,sK1),vabs(sK4,sK5,sK6),sK7),
inference(cnf_transformation,[],[f133]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( visFreeVar(X0,X3)
| vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : vsubst(X0,X1,vabs(X0,X2,X3)) = vabs(X0,X2,X3),
inference(cnf_transformation,[],[f149]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : ~ visFreeVar(X0,vabs(X0,X1,X2)),
inference(cnf_transformation,[],[f181]) ).
tcf(c_256,plain,
~ vtcheck(sK1,vabs(sK4,sK5,sK6),sK7),
inference(demodulation,[status(thm)],[c_49,c_65]) ).
tcf(c_756,plain,
( visFreeVar(sK4,vabs(sK4,sK5,sK6))
| vtcheck(sK1,vabs(sK4,sK5,sK6),sK7) ),
inference(superposition,[status(thm)],[c_51,c_58]) ).
tcf(c_758,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_756,c_79,c_256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM130+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 07:54:55 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.33/1.28 % SZS status Started for theBenchmark.p
% 3.33/1.28 % SZS status Theorem for theBenchmark.p
% 3.33/1.28
% 3.33/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.33/1.28
% 3.33/1.28 % ------ iProver source info
% 3.33/1.28
% 3.33/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.33/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.33/1.28 % git: non_committed_changes: false
% 3.33/1.28
% 3.33/1.28 % ------ Parsing...
% 3.33/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.33/1.28
% 3.33/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.33/1.28
% 3.33/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.33/1.28
% 3.33/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.33/1.28 % ------ Proving...
% 3.33/1.28 % ------ Problem Properties
% 3.33/1.28
% 3.33/1.28 %
% 3.33/1.28 % clauses 32
% 3.33/1.28 % conjectures 2
% 3.33/1.28 % EPR 1
% 3.33/1.28 % Horn 25
% 3.33/1.28 % unary 11
% 3.33/1.28 % binary 15
% 3.33/1.28 % lits 59
% 3.33/1.28 % lits eq 31
% 3.33/1.28 % fd_pure 0
% 3.33/1.28 % fd_pseudo 0
% 3.33/1.28 % fd_cond 0
% 3.33/1.28 % fd_pseudo_cond 14
% 3.33/1.28 % AC symbols 0
% 3.33/1.28
% 3.33/1.28 % ------ Schedule dynamic 5 is on
% 3.33/1.28
% 3.33/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.33/1.28
% 3.33/1.28
% 3.33/1.28 % ------
% 3.33/1.28 % Current options:
% 3.33/1.28 % ------
% 3.33/1.28
% 3.33/1.28
% 3.33/1.28 %
% 3.33/1.28
% 3.33/1.28 % ------ Proving...
% 3.33/1.28 %
% 3.33/1.28
% 3.33/1.28 % SZS status Theorem for theBenchmark.p
% 3.33/1.28
% 3.33/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.33/1.28
% 3.33/1.28
%------------------------------------------------------------------------------