%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET722+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 : n006.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 02:47:57 PM UTC 2026
% Result : Theorem 0.59s 6.17s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 168 ( 3 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 205 ( 80 ~; 76 |; 40 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-5 aty)
% Number of variables : 170 ( 0 sgn 149 !; 21 ?; 42 :)
% 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/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).
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(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( surjective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> surjective(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII13) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( surjective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3) )
=> surjective(X1,X3,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
? [X0,X1,X2,X3,X4] :
( surjective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ surjective(X1,X3,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( surjective(compose_function(X1,X0,X2,X3,X4),X2,X4)
& maps(X1,X3,X4)
& maps(X0,X2,X3)
& ~ surjective(X1,X3,X4) ),
inference(flattening,[],[f33]) ).
fof(f37,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(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f40,plain,
( surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4)
& maps(sK1,sK3,sK4)
& maps(sK0,sK2,sK3)
& ~ surjective(sK1,sK3,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)],[f34]) ).
fof(f42,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,[],[f38]) ).
fof(f43,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,[],[f42]) ).
fof(f44,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,sK6(X0,X1,X3,X5,X6),X6)
& apply(X1,X5,sK6(X0,X1,X3,X5,X6))
& member(sK6(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,[sK6]),skolemize(X8,sK6(X0,X1,X3,X5,X6))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X3] :
( ~ member(X3,X2)
| ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ? [X6] :
( apply(X0,X6,X5)
& member(X6,X1) ) ) )
& ( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ~ surjective(X0,X1,X2)
| ! [X5] :
( ~ member(X5,X2)
| ( apply(X0,sK8(X0,X1,X5),X5)
& member(sK8(X0,X1,X5),X1) ) ) )
& ( ( member(sK7(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X6,sK8(X0,X1,X5))],[f46]) ).
fof(f48,plain,
surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f51,plain,
~ surjective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f55,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,sK6(X0,X1,X3,X5,X6),X6) ),
inference(cnf_transformation,[],[f44]) ).
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)
| member(sK6(X0,X1,X3,X5,X6),X3) ),
inference(cnf_transformation,[],[f44]) ).
fof(f59,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| apply(X0,sK8(X0,X1,X5),X5) ),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
! [X2,X0,X1,X5] :
( ~ surjective(X0,X1,X2)
| ~ member(X5,X2)
| member(sK8(X0,X1,X5),X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f61,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK7(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_49,negated_conjecture,
~ surjective(sK1,sK3,sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,negated_conjecture,
surjective(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK4),
inference(cnf_transformation,[],[f48]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( member(sK6(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,[],[f57]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( apply(X0,sK6(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,[],[f55]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK7(X0,X2,X3)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X3),X1)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK8(X0,X1,X3),X3)
| ~ member(X3,X2)
| ~ surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK4 )
| ( compose_function(sK1,sK0,sK2,sK3,sK4) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_62]) ).
tcf(c_413,plain,
! [X0: $i] :
( member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),sK2)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_412]) ).
tcf(c_906,plain,
! [X0: $i] :
( apply(compose_function(sK1,sK0,sK2,sK3,sK4),sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),X0)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_52,c_63]) ).
tcf(c_938,plain,
! [X0: $i] :
( member(sK6(sK1,sK0,sK3,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),X0),sK3)
| ~ member(X0,sK4)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),sK2) ),
inference(superposition,[status(thm)],[c_906,c_57]) ).
tcf(c_980,plain,
! [X0: $i] :
( member(sK6(sK1,sK0,sK3,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),X0),sK3)
| ~ member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_938,c_413,c_938]) ).
tcf(c_1130,plain,
! [X0: $i] :
( apply(sK1,sK6(sK1,sK0,sK3,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),X0),X0)
| ~ member(X0,sK4)
| ~ member(sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),sK2) ),
inference(superposition,[status(thm)],[c_906,c_59]) ).
tcf(c_1151,plain,
! [X0: $i] :
( apply(sK1,sK6(sK1,sK0,sK3,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,X0),X0),X0)
| ~ member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_1130,c_413,c_1130]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i] :
( surjective(sK1,X0,X1)
| ~ member(sK7(sK1,X0,X1),sK4)
| ~ member(sK6(sK1,sK0,sK3,sK8(compose_function(sK1,sK0,sK2,sK3,sK4),sK2,sK7(sK1,X0,X1)),sK7(sK1,X0,X1)),X0) ),
inference(superposition,[status(thm)],[c_1151,c_60]) ).
tcf(c_1190,plain,
! [X0: $i] :
( surjective(sK1,sK3,X0)
| ~ member(sK7(sK1,sK3,X0),sK4) ),
inference(superposition,[status(thm)],[c_980,c_1159]) ).
tcf(c_1248,plain,
surjective(sK1,sK3,sK4),
inference(superposition,[status(thm)],[c_61,c_1190]) ).
tcf(c_1249,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1248,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET722+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/5.35 % Computer : n006.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.35 % CPULimit : 300
% 0.07/5.35 % WCLimit : 300
% 0.07/5.35 % DateTime : Thu Sep 24 11:46:01 UTC 2026
% 0.07/5.35 % CPUTime :
% 0.07/5.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/5.39 Running first-order theorem proving
% 0.07/5.39 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
% 0.11/5.40
% 0.11/5.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.40
% 0.11/5.40 % Detected problem language: tptp
% 0.11/5.42 % Proving...
% 0.59/6.17 % SZS status Started for theBenchmark.p
% 0.59/6.17 % SZS status Theorem for theBenchmark.p
% 0.59/6.17
% 0.59/6.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.59/6.17
% 0.59/6.17 % ------ iProver source info
% 0.59/6.17
% 0.59/6.17 % git: date: 2026-07-19 20:42:38 +0200
% 0.59/6.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.59/6.17 % git: non_committed_changes: false
% 0.59/6.17
% 0.59/6.17 % ------ Parsing...
% 0.59/6.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.59/6.17
% 0.59/6.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 0.59/6.17
% 0.59/6.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.59/6.17
% 0.59/6.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.59/6.17 % ------ Proving...
% 0.59/6.17 % ------ Problem Properties
% 0.59/6.17
% 0.59/6.17 %
% 0.59/6.17 % clauses 16
% 0.59/6.17 % conjectures 2
% 0.59/6.17 % EPR 3
% 0.59/6.17 % Horn 15
% 0.59/6.17 % unary 2
% 0.59/6.17 % binary 5
% 0.59/6.17 % lits 51
% 0.59/6.17 % lits eq 2
% 0.59/6.17 % fd_pure 0
% 0.59/6.17 % fd_pseudo 0
% 0.59/6.17 % fd_cond 0
% 0.59/6.17 % fd_pseudo_cond 2
% 0.59/6.17 % AC symbols 0
% 0.59/6.17
% 0.59/6.17 % ------ Schedule dynamic 5 is on
% 0.59/6.17
% 0.59/6.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.59/6.17
% 0.59/6.17
% 0.59/6.17 % ------
% 0.59/6.17 % Current options:
% 0.59/6.17 % ------
% 0.59/6.17
% 0.59/6.17
% 0.59/6.17 %
% 0.59/6.17
% 0.59/6.17 % ------ Proving...
% 0.59/6.17 %
% 0.59/6.17
% 0.59/6.17 % SZS status Theorem for theBenchmark.p
% 0.59/6.17
% 0.59/6.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.59/6.18
% 0.59/6.18
%------------------------------------------------------------------------------