%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 03:39:52 PM UTC 2026
% Result : Theorem 0.39s 1.26s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 11 unt; 3 def)
% Number of atoms : 121 ( 3 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 113 ( 40 ~; 29 |; 32 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 34 !; 12 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X2] :
( big_p(X2)
=> ( big_p(h(X2))
& big_p(g(X2)) ) )
& ! [X0] :
? [X1] :
( big_p(X0)
=> ( big_p(X1)
& big_r(X0,g(h(X1))) ) ) )
=> ! [X0] :
( big_p(X0)
=> ? [X1] :
( big_p(X1)
& big_r(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2116) ).
fof(f2,negated_conjecture,
~ ( ( ! [X2] :
( big_p(X2)
=> ( big_p(h(X2))
& big_p(g(X2)) ) )
& ! [X0] :
? [X1] :
( big_p(X0)
=> ( big_p(X1)
& big_r(X0,g(h(X1))) ) ) )
=> ! [X0] :
( big_p(X0)
=> ? [X1] :
( big_p(X1)
& big_r(X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X2] :
( big_p(X2)
=> ( big_p(h(X2))
& big_p(g(X2)) ) )
& ! [X0] :
? [X1] :
( big_p(X0)
=> ( big_p(X1)
& big_r(X0,g(h(X1))) ) ) )
=> ! [X3] :
( big_p(X3)
=> ? [X4] :
( big_p(X4)
& big_r(X3,X4) ) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X2] :
( ~ big_p(X2)
| ( big_p(h(X2))
& big_p(g(X2)) ) )
& ! [X0] :
? [X1] :
( ~ big_p(X0)
| ( big_p(X1)
& big_r(X0,g(h(X1))) ) )
& ? [X3] :
( big_p(X3)
& ! [X4] :
( ~ big_p(X4)
| ~ big_r(X3,X4) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X2] :
( ~ big_p(X2)
| ( big_p(h(X2))
& big_p(g(X2)) ) )
& ! [X0] :
? [X1] :
( ~ big_p(X0)
| ( big_p(X1)
& big_r(X0,g(h(X1))) ) )
& ? [X3] :
( big_p(X3)
& ! [X4] :
( ~ big_p(X4)
| ~ big_r(X3,X4) ) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ! [X4] :
( ~ big_p(X4)
| ( big_p(h(X4))
& big_p(g(X4)) ) )
& ! [X2] :
? [X3] :
( ~ big_p(X2)
| ( big_p(X3)
& big_r(X2,g(h(X3))) ) )
& ? [X0] :
( big_p(X0)
& ! [X1] :
( ~ big_p(X1)
| ~ big_r(X0,X1) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X4] :
( ~ big_p(X4)
| ( big_p(h(X4))
& big_p(g(X4)) ) )
& ! [X2] :
( ~ big_p(X2)
| ( big_p(sK1(X2))
& big_r(X2,g(h(sK1(X2)))) ) )
& big_p(sK0)
& ! [X1] :
( ~ big_p(X1)
| ~ big_r(sK0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X2))],[f6]) ).
fof(f8,plain,
! [X4] :
( ~ big_p(X4)
| big_p(h(X4)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X4] :
( ~ big_p(X4)
| big_p(g(X4)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2] :
( ~ big_p(X2)
| big_p(sK1(X2)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2] :
( ~ big_p(X2)
| big_r(X2,g(h(sK1(X2)))) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
big_p(sK0),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X1] :
( ~ big_p(X1)
| ~ big_r(sK0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ big_p(X0)
| ~ big_r(sK0,X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,negated_conjecture,
big_p(sK0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( big_r(X0,g(h(sK1(X0))))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( big_p(sK1(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( big_p(g(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( big_p(h(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_82,plain,
( ~ big_p(sK0)
| ~ big_p(g(h(sK1(sK0)))) ),
inference(resolution,[status(thm)],[c_49,c_51]) ).
tcf(c_83,plain,
~ big_p(g(h(sK1(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_82,c_50,c_82]) ).
tcf(c_105,definition,
iPr_def_10 = sK1(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_106,definition,
iPr_def_11 = h(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_107,definition,
iPr_def_12 = g(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_108,plain,
~ big_p(iPr_def_12),
inference(demodulation,[status(thm)],[c_83,c_105,c_106,c_107]) ).
tcf(c_109,negated_conjecture,
! [X0: $i] :
( big_p(h(X0))
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_110,negated_conjecture,
! [X0: $i] :
( big_p(g(X0))
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_111,negated_conjecture,
! [X0: $i] :
( big_p(sK1(X0))
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_112,negated_conjecture,
big_p(sK0),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_233,plain,
( big_p(iPr_def_10)
| ~ big_p(sK0) ),
inference(superposition,[status(thm)],[c_105,c_111]) ).
tcf(c_234,plain,
big_p(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_233,c_112]) ).
tcf(c_235,plain,
( big_p(iPr_def_11)
| ~ big_p(iPr_def_10) ),
inference(superposition,[status(thm)],[c_106,c_109]) ).
tcf(c_236,plain,
big_p(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_235,c_234]) ).
tcf(c_237,plain,
( big_p(iPr_def_12)
| ~ big_p(iPr_def_11) ),
inference(superposition,[status(thm)],[c_107,c_110]) ).
tcf(c_238,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_237,c_108,c_236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN365+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 01:04:28 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 0.39/1.26 % SZS status Started for theBenchmark.p
% 0.39/1.26 % SZS status Theorem for theBenchmark.p
% 0.39/1.26
% 0.39/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.39/1.26
% 0.39/1.26 % ------ iProver source info
% 0.39/1.26
% 0.39/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 0.39/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.39/1.26 % git: non_committed_changes: false
% 0.39/1.26
% 0.39/1.26 % ------ Parsing...
% 0.39/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.39/1.26
% 0.39/1.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.39/1.26
% 0.39/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.39/1.26
% 0.39/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.39/1.26 % ------ Proving...
% 0.39/1.26 % ------ Problem Properties
% 0.39/1.26
% 0.39/1.26 %
% 0.39/1.26 % clauses 8
% 0.39/1.26 % conjectures 4
% 0.39/1.26 % EPR 2
% 0.39/1.26 % Horn 8
% 0.39/1.26 % unary 5
% 0.39/1.26 % binary 3
% 0.39/1.26 % lits 11
% 0.39/1.26 % lits eq 3
% 0.39/1.26 % fd_pure 0
% 0.39/1.26 % fd_pseudo 0
% 0.39/1.26 % fd_cond 0
% 0.39/1.26 % fd_pseudo_cond 0
% 0.39/1.26 % AC symbols 0
% 0.39/1.26
% 0.39/1.26 % ------ Schedule dynamic 5 is on
% 0.39/1.26
% 0.39/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.39/1.26
% 0.39/1.26
% 0.39/1.26 % ------
% 0.39/1.26 % Current options:
% 0.39/1.26 % ------
% 0.39/1.26
% 0.39/1.26
% 0.39/1.26 %
% 0.39/1.26
% 0.39/1.26 % ------ Proving...
% 0.39/1.26 %
% 0.39/1.26
% 0.39/1.26 % SZS status Theorem for theBenchmark.p
% 0.39/1.26
% 0.39/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.39/1.26
% 0.39/1.26
%------------------------------------------------------------------------------