%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET734+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 : n010.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 3.75s 1.19s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 156 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 186 ( 74 ~; 65 |; 33 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 7 ( 7 usr; 4 con; 0-5 aty)
% Number of variables : 156 ( 0 sgn 140 !; 16 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(f16,axiom,
! [X0,X1] :
( identity(X0,X1)
<=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).
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/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> surjective(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII25) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3) )
=> surjective(X1,X2,X3) ),
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(f33,plain,
! [X0,X1] :
( identity(X0,X1)
=> ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3)
& ~ surjective(X1,X2,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( identity(compose_function(X1,X0,X3,X2,X3),X3)
& maps(X0,X3,X2)
& maps(X1,X2,X3)
& ~ surjective(X1,X2,X3) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1] :
( ~ identity(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
<=> ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,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(f43,plain,
( identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3)
& maps(sK0,sK3,sK2)
& maps(sK1,sK2,sK3)
& ~ surjective(sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X7] :
( apply(X0,X7,X6)
& apply(X1,X5,X7)
& member(X7,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ? [X8] :
( apply(X0,X8,X6)
& apply(X1,X5,X8)
& member(X8,X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| ( apply(X0,sK5(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK5(X0,X1,X3,X5,X6))
& member(sK5(X0,X1,X3,X5,X6),X3) ) )
& ( ! [X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X1,X5,X7)
| ~ member(X7,X3) )
| apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X8,sK5(X0,X1,X3,X5,X6))],[f46]) ).
fof(f48,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))],[f42]) ).
fof(f49,plain,
identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3),
inference(cnf_transformation,[],[f43]) ).
fof(f52,plain,
~ surjective(sK1,sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ identity(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| apply(X0,sK5(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f47]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
| member(sK5(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK6(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,negated_conjecture,
~ surjective(sK1,sK2,sK3),
inference(cnf_transformation,[],[f52]) ).
tcf(c_52,negated_conjecture,
identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3),
inference(cnf_transformation,[],[f49]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ identity(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK5(X0,X1,X3,X5,X6),X3)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK5(X0,X1,X3,X5,X6),X6)
| ~ member(X6,X4)
| ~ member(X5,X2)
| ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_61,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,[],[f62]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK6(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ( X1 != sK3 )
| ( compose_function(sK1,sK0,sK3,sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_245,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK3,sK2,sK3),X0,X0)
| ~ member(X0,sK3) ),
inference(unflattening,[status(thm)],[c_244]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X1)
| ~ apply(X0,X3,sK6(X0,X1,X2))
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_256,plain,
! [X0: $i] :
( ~ member(X0,sK2)
| ~ apply(sK1,X0,sK6(sK1,sK2,sK3)) ),
inference(unflattening,[status(thm)],[c_255]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK6(X0,X1,X2),X2)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_265,plain,
member(sK6(sK1,sK2,sK3),sK3),
inference(unflattening,[status(thm)],[c_264]) ).
tcf(c_922,plain,
! [X0: $i] :
( member(sK5(sK1,sK0,sK2,X0,X0),sK2)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_245,c_58]) ).
tcf(c_946,plain,
! [X0: $i] :
( apply(sK1,sK5(sK1,sK0,sK2,X0,X0),X0)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_245,c_60]) ).
tcf(c_971,plain,
( ~ member(sK6(sK1,sK2,sK3),sK3)
| ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_946,c_256]) ).
tcf(c_973,plain,
~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_971,c_265]) ).
tcf(c_986,plain,
~ member(sK6(sK1,sK2,sK3),sK3),
inference(superposition,[status(thm)],[c_922,c_973]) ).
tcf(c_987,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_986,c_265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET734+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 : n010.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 11:48:28 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...
% 3.75/1.19 % SZS status Started for theBenchmark.p
% 3.75/1.19 % SZS status Theorem for theBenchmark.p
% 3.75/1.19
% 3.75/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.75/1.19
% 3.75/1.19 % ------ iProver source info
% 3.75/1.19
% 3.75/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.75/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.75/1.19 % git: non_committed_changes: false
% 3.75/1.19
% 3.75/1.19 % ------ Parsing...
% 3.75/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.75/1.19
% 3.75/1.19 % ------ 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 %
% 3.75/1.19
% 3.75/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.75/1.19
% 3.75/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.75/1.19 % ------ Proving...
% 3.75/1.19 % ------ Problem Properties
% 3.75/1.19
% 3.75/1.19 %
% 3.75/1.19 % clauses 13
% 3.75/1.19 % conjectures 0
% 3.75/1.19 % EPR 2
% 3.75/1.19 % Horn 13
% 3.75/1.19 % unary 1
% 3.75/1.19 % binary 6
% 3.75/1.19 % lits 43
% 3.75/1.19 % lits eq 2
% 3.75/1.19 % fd_pure 0
% 3.75/1.19 % fd_pseudo 0
% 3.75/1.19 % fd_cond 0
% 3.75/1.19 % fd_pseudo_cond 2
% 3.75/1.19 % AC symbols 0
% 3.75/1.19
% 3.75/1.19 % ------ Schedule dynamic 5 is on
% 3.75/1.19
% 3.75/1.19 % ------ no conjectures: strip conj schedule
% 3.75/1.19
% 3.75/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.75/1.19
% 3.75/1.19
% 3.75/1.19 % ------
% 3.75/1.19 % Current options:
% 3.75/1.19 % ------
% 3.75/1.19
% 3.75/1.19
% 3.75/1.19 %
% 3.75/1.19
% 3.75/1.19 % ------ Proving...
% 3.75/1.19 %
% 3.75/1.19
% 3.75/1.19 % SZS status Theorem for theBenchmark.p
% 3.75/1.19
% 3.75/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.19
% 3.75/1.19
%------------------------------------------------------------------------------