%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET731+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:47:59 PM UTC 2026
% Result : Theorem 4.20s 1.43s
% Output : CNFRefutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 143 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 66 ~; 55 |; 37 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 116 ( 0 sgn 95 !; 21 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> surjective(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII22) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> surjective(X1,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ surjective(X1,X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ surjective(X1,X2,X4) ),
inference(flattening,[],[f35]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f41,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(X1,X5,X6)
| apply(X0,X5,X6) )
& ( ~ apply(X0,X5,X6)
| apply(X1,X5,X6) ) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ surjective(X1,X2,X4) ),
inference(nnf_transformation,[],[f36]) ).
fof(f42,plain,
( ! [X5,X6] :
( ~ member(X6,sK4)
| ~ member(X5,sK2)
| ( ( ~ apply(sK1,X5,X6)
| apply(sK0,X5,X6) )
& ( ~ apply(sK0,X5,X6)
| apply(sK1,X5,X6) ) ) )
& sK4 = image2(sK0,sK2)
& subset(sK4,sK3)
& maps(sK0,sK2,sK3)
& ~ surjective(sK1,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( member(sK6(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK6(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f40]) ).
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,sK7(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f46]) ).
fof(f49,plain,
! [X6,X5] :
( ~ member(X6,sK4)
| ~ member(X5,sK2)
| ~ apply(sK0,X5,X6)
| apply(sK1,X5,X6) ),
inference(cnf_transformation,[],[f42]) ).
fof(f50,plain,
sK4 = image2(sK0,sK2),
inference(cnf_transformation,[],[f42]) ).
fof(f53,plain,
~ surjective(sK1,sK2,sK4),
inference(cnf_transformation,[],[f42]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK6(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| apply(X0,sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ surjective(sK1,sK2,sK4),
inference(cnf_transformation,[],[f53]) ).
tcf(c_52,negated_conjecture,
image2(sK0,sK2) = sK4,
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK1,X0,X1)
| ~ member(X1,sK4)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK6(X0,X2,X3)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X1,X2,X0),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,sK7(X1,X2,X0),X0)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X1)
| ~ apply(X0,X3,sK6(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_245,plain,
! [X0: $i] :
( ~ member(X0,sK2)
| ~ apply(sK1,X0,sK6(sK1,sK2,sK4)) ),
inference(unflattening,[status(thm)],[c_244]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X2)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_254,plain,
member(sK6(sK1,sK2,sK4),sK4),
inference(unflattening,[status(thm)],[c_253]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK7(sK0,X0,X1),X1)
| ~ member(X1,sK4)
| ~ member(X1,image2(sK0,X0))
| ~ member(sK7(sK0,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_63,c_53]) ).
tcf(c_841,plain,
! [X0: $i] :
( ~ member(sK6(sK1,sK2,sK4),sK4)
| ~ member(sK6(sK1,sK2,sK4),image2(sK0,X0))
| ~ member(sK7(sK0,X0,sK6(sK1,sK2,sK4)),sK2) ),
inference(superposition,[status(thm)],[c_734,c_245]) ).
tcf(c_846,plain,
! [X0: $i] :
( ~ member(sK6(sK1,sK2,sK4),image2(sK0,X0))
| ~ member(sK7(sK0,X0,sK6(sK1,sK2,sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_841,c_254]) ).
tcf(c_872,plain,
~ member(sK6(sK1,sK2,sK4),image2(sK0,sK2)),
inference(superposition,[status(thm)],[c_62,c_846]) ).
tcf(c_873,plain,
~ member(sK6(sK1,sK2,sK4),sK4),
inference(light_normalisation,[status(thm)],[c_872,c_52]) ).
tcf(c_874,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_873,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET731+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 11:49:33 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.24/0.51
% 0.24/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.51
% 0.24/0.52 % Detected problem language: tptp
% 0.24/0.53 % Proving...
% 4.20/1.43 % SZS status Started for theBenchmark.p
% 4.20/1.43 % SZS status Theorem for theBenchmark.p
% 4.20/1.43
% 4.20/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.20/1.43
% 4.20/1.43 % ------ iProver source info
% 4.20/1.43
% 4.20/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 4.20/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.20/1.43 % git: non_committed_changes: false
% 4.20/1.43
% 4.20/1.43 % ------ Parsing...
% 4.20/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.20/1.43
% 4.20/1.43 % ------ 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: 4 0s sf_e pe_s pe_e %
% 4.20/1.43
% 4.20/1.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.20/1.43
% 4.20/1.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.20/1.43 % ------ Proving...
% 4.20/1.43 % ------ Problem Properties
% 4.20/1.43
% 4.20/1.43 %
% 4.20/1.43 % clauses 12
% 4.20/1.43 % conjectures 3
% 4.20/1.43 % EPR 4
% 4.20/1.43 % Horn 12
% 4.20/1.43 % unary 2
% 4.20/1.43 % binary 6
% 4.20/1.43 % lits 31
% 4.20/1.43 % lits eq 2
% 4.20/1.43 % fd_pure 0
% 4.20/1.43 % fd_pseudo 0
% 4.20/1.43 % fd_cond 0
% 4.20/1.43 % fd_pseudo_cond 1
% 4.20/1.43 % AC symbols 0
% 4.20/1.43
% 4.20/1.43 % ------ Schedule dynamic 5 is on
% 4.20/1.43
% 4.20/1.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.20/1.43
% 4.20/1.43
% 4.20/1.43 % ------
% 4.20/1.43 % Current options:
% 4.20/1.43 % ------
% 4.20/1.43
% 4.20/1.43
% 4.20/1.43 %
% 4.20/1.43
% 4.20/1.43 % ------ Proving...
% 4.20/1.43 %
% 4.20/1.43
% 4.20/1.43 % SZS status Theorem for theBenchmark.p
% 4.20/1.43
% 4.20/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.20/1.43
% 4.20/1.43
%------------------------------------------------------------------------------