%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN415+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 : n018.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 03:40:00 PM UTC 2026
% Result : Theorem 2.19s 1.27s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 57 ( 5 unt; 1 def)
% Number of atoms : 243 ( 52 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 254 ( 98 ~; 109 |; 37 &)
% ( 3 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 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 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 84 ( 0 sgn 61 !; 23 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X1,X2] :
( ( f(X2)
& f(X1) )
=> X1 = X2 )
& ? [X0] : f(X0) )
<=> ? [X3] :
( ! [X4] :
( f(X4)
=> X3 = X4 )
& f(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish317) ).
fof(f2,negated_conjecture,
~ ( ( ! [X1,X2] :
( ( f(X2)
& f(X1) )
=> X1 = X2 )
& ? [X0] : f(X0) )
<=> ? [X3] :
( ! [X4] :
( f(X4)
=> X3 = X4 )
& f(X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [X1,X2] :
( ~ f(X2)
| ~ f(X1)
| X1 = X2 )
& ? [X0] : f(X0) )
<~> ? [X3] :
( ! [X4] :
( ~ f(X4)
| X3 = X4 )
& f(X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ! [X1,X2] :
( ~ f(X2)
| ~ f(X1)
| X1 = X2 )
& ? [X0] : f(X0) )
<~> ? [X3] :
( ! [X4] :
( ~ f(X4)
| X3 = X4 )
& f(X3) ) ),
inference(flattening,[],[f3]) ).
fof(f11,plain,
( ( sP0
| ? [X3] :
( ! [X4] :
( ~ f(X4)
| X3 = X4 )
& f(X3) ) )
& ( ~ sP0
| ! [X3] :
( ? [X4] :
( f(X4)
& X3 != X4 )
| ~ f(X3) ) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f12,plain,
( ( sP0
| ? [X2] :
( ! [X3] :
( ~ f(X3)
| X2 = X3 )
& f(X2) ) )
& ( ~ sP0
| ! [X0] :
( ? [X1] :
( f(X1)
& X0 != X1 )
| ~ f(X0) ) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( sP0
| ( ! [X3] :
( ~ f(X3)
| sK5 = X3 )
& f(sK5) ) )
& ( ~ sP0
| ! [X0] :
( ( f(sK4(X0))
& sK4(X0) != X0 )
| ~ f(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X2,sK5)],[f12]) ).
fof(f19,plain,
! [X3] :
( sP0
| ~ f(X3)
| sK5 = X3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
( sP0
| f(sK5) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0] :
( ~ sP0
| f(sK4(X0))
| ~ f(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0] :
( ~ sP0
| sK4(X0) != X0
| ~ f(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( ~ sP0
| ~ f(X0)
| ( sK4(X0) != X0 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( f(sK4(X0))
| ~ sP0
| ~ f(X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_56,negated_conjecture,
( sP0
| f(sK5) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( sP0
| ( X0 = sK5 )
| ~ f(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_507,negated_conjecture,
! [X0: $i] :
( sP0
| ( X0 = sK5 )
| ~ f(X0) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_508,negated_conjecture,
( sP0
| f(sK5) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_509,negated_conjecture,
! [X0: $i] :
( f(sK4(X0))
| ~ sP0
| ~ f(X0) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_510,negated_conjecture,
! [X0: $i] :
( ~ sP0
| ~ f(X0)
| ( sK4(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_899,plain,
( ~ sP0
| ~ f(sK3)
| ( sK4(sK3) != sK3 ) ),
inference(instantiation,[status(thm)],[c_510]) ).
tcf(c_948,plain,
! [X0: $i] :
( ( sK1 = sK2 )
| ( sK2 != X0 )
| ( sK1 != X0 ) ),
inference(instantiation,[status(thm)],[c_513]) ).
tcf(c_974,plain,
( ( sK1 = sK2 )
| ( sK2 != sK5 )
| ( sK1 != sK5 ) ),
inference(instantiation,[status(thm)],[c_948]) ).
fof(f5,definition,
( sP0
<=> ( ! [X1,X2] :
( ~ f(X2)
| ~ f(X1)
| X1 = X2 )
& ? [X0] : f(X0) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,plain,
( sP0
<~> ? [X3] :
( ! [X4] :
( ~ f(X4)
| X3 = X4 )
& f(X3) ) ),
inference(definition_folding,[],[f4,f5]) ).
fof(f7,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( ~ f(X2)
| ~ f(X1)
| X1 = X2 )
& ? [X0] : f(X0) ) )
& ( ? [X1,X2] :
( f(X2)
& f(X1)
& X1 != X2 )
| ! [X0] : ~ f(X0)
| sP0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f8,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( ~ f(X2)
| ~ f(X1)
| X1 = X2 )
& ? [X0] : f(X0) ) )
& ( ? [X1,X2] :
( f(X2)
& f(X1)
& X1 != X2 )
| ! [X0] : ~ f(X0)
| sP0 ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
( ( ~ sP0
| ( ! [X4,X5] :
( ~ f(X5)
| ~ f(X4)
| X4 = X5 )
& ? [X3] : f(X3) ) )
& ( ? [X1,X2] :
( f(X2)
& f(X1)
& X1 != X2 )
| ! [X0] : ~ f(X0)
| sP0 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ~ sP0
| ( ! [X4,X5] :
( ~ f(X5)
| ~ f(X4)
| X4 = X5 )
& f(sK3) ) )
& ( ( f(sK2)
& f(sK1)
& sK1 != sK2 )
| ! [X0] : ~ f(X0)
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9]) ).
fof(f14,plain,
! [X4,X5] :
( ~ sP0
| ~ f(X5)
| ~ f(X4)
| X4 = X5 ),
inference(cnf_transformation,[],[f10]) ).
fof(f15,plain,
( ~ sP0
| f(sK3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0] :
( f(sK2)
| ~ f(X0)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0] :
( f(sK1)
| ~ f(X0)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0] :
( sK1 != sK2
| ~ f(X0)
| sP0 ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_49,plain,
! [X0: $i] :
( sP0
| ~ f(X0)
| ( sK1 != sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i] :
( sP0
| f(sK1)
| ~ f(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_51,plain,
! [X0: $i] :
( sP0
| f(sK2)
| ~ f(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,plain,
( f(sK3)
| ~ sP0 ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ sP0
| ~ f(X1)
| ~ f(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_503,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ f(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_51]) ).
tcf(c_504,plain,
( iPr_def_10
| sP0
| f(sK2) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_51]) ).
tcf(c_505,plain,
( iPr_def_10
| sP0
| f(sK1) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_50]) ).
tcf(c_506,plain,
( iPr_def_10
| sP0
| ( sK1 != sK2 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_49]) ).
tcf(c_693,plain,
( iPr_def_10
| sP0
| ( sK2 = sK5 ) ),
inference(superposition,[status(thm)],[c_504,c_507]) ).
tcf(c_709,plain,
( iPr_def_10
| sP0
| ( sK1 = sK5 ) ),
inference(superposition,[status(thm)],[c_505,c_507]) ).
tcf(c_729,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ sP0
| ~ f(X0) ),
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_747,plain,
( ~ iPr_def_10
| ~ sP0 ),
inference(superposition,[status(thm)],[c_52,c_503]) ).
tcf(c_749,plain,
( sP0
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_508,c_503]) ).
tcf(c_754,plain,
~ iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_749,c_747]) ).
tcf(c_756,plain,
( sP0
| ( sK1 != sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_506,c_754]) ).
tcf(c_978,plain,
sP0,
inference(global_subsumption_just,[status(thm)],[c_756,c_506,c_693,c_709,c_754,c_974]) ).
tcf(c_988,plain,
! [X0: $i] :
( f(sK4(X0))
| ~ f(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_509,c_978]) ).
tcf(c_991,plain,
f(sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_978]) ).
tcf(c_1035,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ f(X0) ),
inference(global_subsumption_just,[status(thm)],[c_729,c_506,c_693,c_709,c_729,c_754,c_974]) ).
tcf(c_1043,plain,
! [X0: $i] :
( ( sK4(X0) = sK3 )
| ~ f(X0) ),
inference(superposition,[status(thm)],[c_988,c_1035]) ).
tcf(c_1055,plain,
sK4(sK3) = sK3,
inference(superposition,[status(thm)],[c_991,c_1043]) ).
tcf(c_1059,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1055,c_978,c_899,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 01:08:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.19/1.27 % SZS status Started for theBenchmark.p
% 2.19/1.27 % SZS status Theorem for theBenchmark.p
% 2.19/1.27
% 2.19/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/1.27
% 2.19/1.27 % ------ iProver source info
% 2.19/1.27
% 2.19/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/1.27 % git: non_committed_changes: false
% 2.19/1.27
% 2.19/1.27 % ------ Parsing...
% 2.19/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/1.27
% 2.19/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.19/1.27 % ------ Proving...
% 2.19/1.27 % ------ Problem Properties
% 2.19/1.27
% 2.19/1.27 %
% 2.19/1.27 % clauses 10
% 2.19/1.27 % conjectures 4
% 2.19/1.27 % EPR 8
% 2.19/1.27 % Horn 5
% 2.19/1.27 % unary 0
% 2.19/1.27 % binary 3
% 2.19/1.27 % lits 28
% 2.19/1.27 % lits eq 4
% 2.19/1.27 % fd_pure 0
% 2.19/1.27 % fd_pseudo 0
% 2.19/1.27 % fd_cond 1
% 2.19/1.27 % fd_pseudo_cond 1
% 2.19/1.27 % AC symbols 0
% 2.19/1.27
% 2.19/1.27 % ------ Schedule dynamic 5 is on
% 2.19/1.27
% 2.19/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.19/1.27
% 2.19/1.27
% 2.19/1.27 % ------
% 2.19/1.27 % Current options:
% 2.19/1.27 % ------
% 2.19/1.27
% 2.19/1.27
% 2.19/1.27 %
% 2.19/1.27
% 2.19/1.27 % ------ Proving...
% 2.19/1.27 %
% 2.19/1.27
% 2.19/1.27 % SZS status Theorem for theBenchmark.p
% 2.19/1.27
% 2.19/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.27
% 2.19/1.27
%------------------------------------------------------------------------------