%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN078+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 : n014.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 03:39:07 PM UTC 2026
% Result : Theorem 0.44s 1.28s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 40 ( 14 unt; 1 def)
% Number of atoms : 112 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 115 ( 47 ~; 47 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 26 !; 8 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ? [X1] :
( X0 = f(X1)
& big_p(X1) )
=> big_p(X0) )
<=> ! [X2] :
( big_p(X2)
=> big_p(f(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ? [X1] :
( X0 = f(X1)
& big_p(X1) )
=> big_p(X0) )
<=> ! [X2] :
( big_p(X2)
=> big_p(f(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( ! [X1] :
( f(X1) != X0
| ~ big_p(X1) )
| big_p(X0) )
<~> ! [X2] :
( ~ big_p(X2)
| big_p(f(X2)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ! [X0] :
( ! [X1] :
( f(X1) != X0
| ~ big_p(X1) )
| big_p(X0) )
| ! [X2] :
( ~ big_p(X2)
| big_p(f(X2)) ) )
& ( ? [X0] :
( ? [X1] :
( f(X1) = X0
& big_p(X1) )
& ~ big_p(X0) )
| ? [X2] :
( big_p(X2)
& ~ big_p(f(X2)) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X4] :
( ! [X5] :
( f(X5) != X4
| ~ big_p(X5) )
| big_p(X4) )
| ! [X3] :
( ~ big_p(X3)
| big_p(f(X3)) ) )
& ( ? [X1] :
( ? [X2] :
( f(X2) = X1
& big_p(X2) )
& ~ big_p(X1) )
| ? [X0] :
( big_p(X0)
& ~ big_p(f(X0)) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ( ! [X4] :
( ! [X5] :
( f(X5) != X4
| ~ big_p(X5) )
| big_p(X4) )
| ! [X3] :
( ~ big_p(X3)
| big_p(f(X3)) ) )
& ( ( sK1 = f(sK2)
& big_p(sK2)
& ~ big_p(sK1) )
| ( big_p(sK0)
& ~ big_p(f(sK0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
fof(f7,plain,
! [X3,X4,X5] :
( f(X5) != X4
| ~ big_p(X5)
| big_p(X4)
| ~ big_p(X3)
| big_p(f(X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
( sK1 = f(sK2)
| big_p(sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
( big_p(sK2)
| big_p(sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
( ~ big_p(sK1)
| big_p(sK0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
( sK1 = f(sK2)
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
( big_p(sK2)
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
( ~ big_p(sK1)
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X3,X5] :
( ~ big_p(X5)
| big_p(f(X5))
| ~ big_p(X3)
| big_p(f(X3)) ),
inference(equality_resolution,[],[f7]) ).
tcf(c_49,negated_conjecture,
( ~ big_p(sK1)
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,negated_conjecture,
( big_p(sK2)
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,negated_conjecture,
( ( f(sK2) = sK1 )
| ~ big_p(f(sK0)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,negated_conjecture,
( big_p(sK0)
| ~ big_p(sK1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_53,negated_conjecture,
( big_p(sK2)
| big_p(sK0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_54,negated_conjecture,
( big_p(sK0)
| ( f(sK2) = sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i] :
( big_p(f(X1))
| big_p(f(X0))
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_56,plain,
( big_p(f(sK0))
| ~ big_p(sK0) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_57,negated_conjecture,
big_p(sK2),
inference(global_subsumption_just,[status(thm)],[c_53,c_53,c_50,c_56]) ).
tcf(c_59,negated_conjecture,
~ big_p(sK1),
inference(global_subsumption_just,[status(thm)],[c_52,c_52,c_49,c_56]) ).
tcf(c_61,negated_conjecture,
big_p(sK2),
inference(global_subsumption_just,[status(thm)],[c_50,c_57]) ).
tcf(c_63,negated_conjecture,
f(sK2) = sK1,
inference(global_subsumption_just,[status(thm)],[c_54,c_54,c_51,c_56]) ).
tcf(c_65,negated_conjecture,
~ big_p(sK1),
inference(global_subsumption_just,[status(thm)],[c_49,c_59]) ).
tcf(c_67,negated_conjecture,
f(sK2) = sK1,
inference(global_subsumption_just,[status(thm)],[c_51,c_63]) ).
tcf(c_115,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| big_p(f(X0))
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_55]) ).
tcf(c_116,negated_conjecture,
iPr_def_10,
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).
tcf(c_117,definition,
iPr_def_11 = f(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_118,negated_conjecture,
iPr_def_11 = sK1,
inference(demodulation,[status(thm)],[c_67,c_117]) ).
tcf(c_119,negated_conjecture,
~ big_p(sK1),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_120,negated_conjecture,
big_p(sK2),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_121,negated_conjecture,
iPr_def_10,
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_123,negated_conjecture,
! [X0: $i] :
( big_p(f(X0))
| ~ iPr_def_10
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_198,plain,
~ big_p(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_119,c_118]) ).
tcf(c_199,negated_conjecture,
! [X0: $i] :
( big_p(f(X0))
| ~ big_p(X0) ),
inference(global_subsumption_just,[status(thm)],[c_123,c_121,c_123]) ).
tcf(c_203,plain,
( big_p(iPr_def_11)
| ~ big_p(sK2) ),
inference(superposition,[status(thm)],[c_117,c_199]) ).
tcf(c_204,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_203,c_198,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:06:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 0.44/1.28 % SZS status Started for theBenchmark.p
% 0.44/1.28 % SZS status Theorem for theBenchmark.p
% 0.44/1.28
% 0.44/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/1.28
% 0.44/1.28 % ------ iProver source info
% 0.44/1.28
% 0.44/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/1.28 % git: non_committed_changes: false
% 0.44/1.28
% 0.44/1.28 % ------ Parsing...
% 0.44/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.44/1.28
% 0.44/1.28 % ------ Preprocessing... sf_s rm: 2 0s sf_e sf_s rm: 0 0s sf_e
% 0.44/1.28 % ------ Proving...
% 0.44/1.28 % ------ Problem Properties
% 0.44/1.28
% 0.44/1.28 %
% 0.44/1.28 % clauses 6
% 0.44/1.28 % conjectures 5
% 0.44/1.28 % EPR 4
% 0.44/1.28 % Horn 6
% 0.44/1.28 % unary 5
% 0.44/1.28 % binary 0
% 0.44/1.28 % lits 8
% 0.44/1.28 % lits eq 2
% 0.44/1.28 % fd_pure 0
% 0.44/1.28 % fd_pseudo 0
% 0.44/1.28 % fd_cond 0
% 0.44/1.28 % fd_pseudo_cond 0
% 0.44/1.28 % AC symbols 0
% 0.44/1.28
% 0.44/1.28 % ------ Schedule dynamic 5 is on
% 0.44/1.28
% 0.44/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.44/1.28
% 0.44/1.28
% 0.44/1.28 % ------
% 0.44/1.28 % Current options:
% 0.44/1.28 % ------
% 0.44/1.28
% 0.44/1.28
% 0.44/1.28 %
% 0.44/1.28
% 0.44/1.28 % ------ Proving...
% 0.44/1.28 %
% 0.44/1.28
% 0.44/1.28 % SZS status Theorem for theBenchmark.p
% 0.44/1.28
% 0.44/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.28
% 0.44/1.28
%------------------------------------------------------------------------------