%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 03:39:05 PM UTC 2026
% Result : Theorem 1.07s 1.18s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 3 unt; 1 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 146 ( 57 ~; 53 |; 32 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 0 sgn 44 !; 8 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( ! [X1] :
( ( big_h(X0,X1)
& big_g(X1) )
=> big_j(X0,X1) )
& big_f(X0) )
=> ! [X2] :
( big_k(X2)
& big_h(X0,X2)
& big_g(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_1) ).
fof(f2,axiom,
~ ? [X0] :
( big_k(X0)
& big_l(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_2) ).
fof(f3,axiom,
? [X0] :
( ! [X2] :
( ( big_h(X0,X2)
& big_g(X2) )
=> big_j(X0,X2) )
& ! [X1] :
( big_h(X0,X1)
=> big_l(X1) )
& big_f(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel45_3) ).
fof(f6,plain,
! [X0] :
( ? [X1] :
( big_h(X0,X1)
& big_g(X1)
& ~ big_j(X0,X1) )
| ~ big_f(X0)
| ! [X2] :
( big_k(X2)
& big_h(X0,X2)
& big_g(X2) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( big_h(X0,X1)
& big_g(X1)
& ~ big_j(X0,X1) )
| ~ big_f(X0)
| ! [X2] :
( big_k(X2)
& big_h(X0,X2)
& big_g(X2) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_l(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0] :
( ! [X2] :
( ~ big_h(X0,X2)
| ~ big_g(X2)
| big_j(X0,X2) )
& ! [X1] :
( ~ big_h(X0,X1)
| big_l(X1) )
& big_f(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ! [X2] :
( ~ big_h(X0,X2)
| ~ big_g(X2)
| big_j(X0,X2) )
& ! [X1] :
( ~ big_h(X0,X1)
| big_l(X1) )
& big_f(X0) ),
inference(flattening,[],[f9]) ).
fof(f16,plain,
! [X0] :
( sP0(X0)
| ~ big_f(X0)
| ! [X1] :
( big_k(X1)
& big_h(X0,X1)
& big_g(X1) ) ),
inference(rectify,[],[f13]) ).
fof(f17,plain,
( ! [X2] :
( ~ big_h(sK2,X2)
| ~ big_g(X2)
| big_j(sK2,X2) )
& ! [X1] :
( ~ big_h(sK2,X1)
| big_l(X1) )
& big_f(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( sP0(X0)
| ~ big_f(X0)
| big_k(X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( sP0(X0)
| ~ big_f(X0)
| big_h(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0] :
( ~ big_k(X0)
| ~ big_l(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X2] :
( ~ big_h(sK2,X2)
| ~ big_g(X2)
| big_j(sK2,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X1] :
( ~ big_h(sK2,X1)
| big_l(X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
big_f(sK2),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( sP0(X0)
| big_h(X0,X1)
| ~ big_f(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( big_k(X1)
| sP0(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i] :
( ~ big_l(X0)
| ~ big_k(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
big_f(sK2),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i] :
( big_l(X0)
| ~ big_h(sK2,X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i] :
( big_j(sK2,X0)
| ~ big_g(X0)
| ~ big_h(sK2,X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_66,plain,
( big_k(sK2)
| sP0(sK2)
| ~ big_f(sK2) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_69,plain,
( sP0(sK2)
| big_h(sK2,sK2)
| ~ big_f(sK2) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_126,plain,
! [X0: $i] :
( ~ big_k(X0)
| ~ big_h(sK2,X0) ),
inference(resolution,[status(thm)],[c_57,c_55]) ).
tcf(c_127,plain,
( ~ big_k(sK2)
| ~ big_h(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_126]) ).
fof(f12,definition,
! [X0] :
( ~ sP0(X0)
| ? [X1] :
( big_h(X0,X1)
& big_g(X1)
& ~ big_j(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f13,plain,
! [X0] :
( sP0(X0)
| ~ big_f(X0)
| ! [X2] :
( big_k(X2)
& big_h(X0,X2)
& big_g(X2) ) ),
inference(definition_folding,[],[f7,f12]) ).
fof(f14,plain,
! [X0] :
( ~ sP0(X0)
| ? [X1] :
( big_h(X0,X1)
& big_g(X1)
& ~ big_j(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ~ sP0(X0)
| ( big_h(X0,sK1(X0))
& big_g(sK1(X0))
& ~ big_j(X0,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f14]) ).
fof(f19,plain,
! [X0] :
( ~ sP0(X0)
| big_h(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0] :
( ~ sP0(X0)
| big_g(sK1(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0] :
( ~ sP0(X0)
| ~ big_j(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_49,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ big_j(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i] :
( big_g(sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i] :
( big_h(X0,sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_64,plain,
( big_g(sK1(sK2))
| ~ sP0(sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_68,plain,
( big_h(sK2,sK1(sK2))
| ~ sP0(sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_136,plain,
( ~ sP0(sK2)
| ~ big_g(sK1(sK2))
| ~ big_h(sK2,sK1(sK2)) ),
inference(resolution,[status(thm)],[c_49,c_58]) ).
tcf(c_139,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_136,c_127,c_69,c_68,c_66,c_64,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN069+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 00:06:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.07/1.18 % SZS status Started for theBenchmark.p
% 1.07/1.18 % SZS status Theorem for theBenchmark.p
% 1.07/1.18
% 1.07/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.07/1.18
% 1.07/1.18 % ------ iProver source info
% 1.07/1.18
% 1.07/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.07/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.07/1.18 % git: non_committed_changes: false
% 1.07/1.18
% 1.07/1.18 % ------ Parsing...
% 1.07/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.07/1.18
% 1.07/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s%
% 1.07/1.18
% 1.07/1.18 % SZS status Theorem for theBenchmark.p
% 1.07/1.18
% 1.07/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.07/1.18
% 1.07/1.18
%------------------------------------------------------------------------------