%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET763+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:48:31 PM UTC 2026
% Result : Theorem 4.32s 1.28s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 70 ( 20 unt; 0 def)
% Number of atoms : 234 ( 13 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 270 ( 106 ~; 93 |; 52 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 184 ( 0 sgn 166 !; 18 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X2)
& member(X5,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X6)
& apply(X0,X3,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( equal_set(image2(X0,X3),empty_set)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> equal_set(X3,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa13) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( equal_set(image2(X0,X3),empty_set)
& subset(X3,X1)
& maps(X0,X1,X2) )
=> equal_set(X3,empty_set) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( equal_set(image2(X0,X3),empty_set)
& subset(X3,X1)
& maps(X0,X1,X2)
& ~ equal_set(X3,empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3] :
( equal_set(image2(X0,X3),empty_set)
& subset(X3,X1)
& maps(X0,X1,X2)
& ~ equal_set(X3,empty_set) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( equal_set(image2(sK0,sK3),empty_set)
& subset(sK3,sK1)
& maps(sK0,sK1,sK2)
& ~ equal_set(sK3,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK4(X0,X1),X0)
& ~ member(sK4(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ equal_set(X0,X1)
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK5(X0,X2,X3))
& member(sK5(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X2,X3))],[f37]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f46]) ).
fof(f48,plain,
equal_set(image2(sK0,sK3),empty_set),
inference(cnf_transformation,[],[f38]) ).
fof(f49,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f50,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f38]) ).
fof(f51,plain,
~ equal_set(sK3,empty_set),
inference(cnf_transformation,[],[f38]) ).
fof(f52,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f58,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK5(X0,X2,X3)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ equal_set(sK3,empty_set),
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,negated_conjecture,
subset(sK3,sK1),
inference(cnf_transformation,[],[f49]) ).
tcf(c_52,negated_conjecture,
equal_set(image2(sK0,sK3),empty_set),
inference(cnf_transformation,[],[f48]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_59,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f58]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,image2(X0,X3))
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X1,X2,X0),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != empty_set )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_238,plain,
( ~ subset(empty_set,sK3)
| ~ subset(sK3,empty_set) ),
inference(unflattening,[status(thm)],[c_237]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( X1 != empty_set )
| ( image2(sK0,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_251,plain,
subset(image2(sK0,sK3),empty_set),
inference(unflattening,[status(thm)],[c_250]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK5(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_61]) ).
tcf(c_283,plain,
! [X0: $i] :
( apply(sK0,X0,sK5(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_282]) ).
tcf(c_699,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_54,c_59]) ).
tcf(c_700,plain,
~ subset(sK3,empty_set),
inference(backward_subsumption_resolution,[status(thm)],[c_238,c_699]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK4(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i] : ~ member(X0,image2(X1,empty_set)),
inference(superposition,[status(thm)],[c_64,c_59]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] : ~ member(X0,image2(X1,image2(X2,empty_set))),
inference(superposition,[status(thm)],[c_64,c_722]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] :
( member(sK5(sK0,sK2,X0),image2(sK0,X1))
| ~ member(X0,sK1)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_283,c_63]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ~ member(X0,image2(X1,image2(X2,image2(X3,empty_set)))),
inference(superposition,[status(thm)],[c_64,c_728]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK5(sK0,sK2,X2),X1)
| ~ member(X2,sK1)
| ~ member(X2,X0)
| ~ subset(image2(sK0,X0),X1) ),
inference(superposition,[status(thm)],[c_870,c_55]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_708,c_59]) ).
tcf(c_1079,plain,
! [X0: $i] : subset(image2(sK0,sK3),X0),
inference(superposition,[status(thm)],[c_251,c_1033]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] :
( member(sK5(sK0,sK2,X0),X1)
| ~ member(X0,sK1)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_1079,c_947]) ).
tcf(c_1183,plain,
! [X0: $i] :
( ~ member(X0,sK1)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_1165,c_884]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ subset(X0,sK1)
| ~ member(sK4(X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_708,c_1183]) ).
tcf(c_1480,plain,
! [X0: $i] :
( subset(sK3,X0)
| ~ subset(sK3,sK1) ),
inference(superposition,[status(thm)],[c_54,c_1365]) ).
tcf(c_1482,plain,
! [X0: $i] : subset(sK3,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1480,c_51]) ).
tcf(c_1486,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_700,c_1482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET763+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:53:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.32/1.28 % SZS status Started for theBenchmark.p
% 4.32/1.28 % SZS status Theorem for theBenchmark.p
% 4.32/1.28
% 4.32/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.32/1.28
% 4.32/1.28 % ------ iProver source info
% 4.32/1.28
% 4.32/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.32/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.32/1.28 % git: non_committed_changes: false
% 4.32/1.28
% 4.32/1.28 % ------ Parsing...
% 4.32/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.32/1.28
% 4.32/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.32/1.28
% 4.32/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.32/1.28
% 4.32/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.32/1.28 % ------ Proving...
% 4.32/1.28 % ------ Problem Properties
% 4.32/1.28
% 4.32/1.28 %
% 4.32/1.28 % clauses 15
% 4.32/1.28 % conjectures 1
% 4.32/1.28 % EPR 5
% 4.32/1.28 % Horn 14
% 4.32/1.28 % unary 5
% 4.32/1.28 % binary 7
% 4.32/1.28 % lits 31
% 4.32/1.28 % lits eq 2
% 4.32/1.28 % fd_pure 0
% 4.32/1.28 % fd_pseudo 0
% 4.32/1.28 % fd_cond 0
% 4.32/1.28 % fd_pseudo_cond 1
% 4.32/1.28 % AC symbols 0
% 4.32/1.28
% 4.32/1.28 % ------ Schedule dynamic 5 is on
% 4.32/1.28
% 4.32/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.32/1.28
% 4.32/1.28
% 4.32/1.28 % ------
% 4.32/1.28 % Current options:
% 4.32/1.28 % ------
% 4.32/1.28
% 4.32/1.28
% 4.32/1.28 %
% 4.32/1.28
% 4.32/1.28 % ------ Proving...
% 4.32/1.28 %
% 4.32/1.28
% 4.32/1.28 % SZS status Theorem for theBenchmark.p
% 4.32/1.28
% 4.32/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.32/1.28
% 4.32/1.28
%------------------------------------------------------------------------------