%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 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 03:40:47 PM UTC 2026
% Result : Theorem 1.67s 1.07s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 8
% Syntax : Number of formulae : 176 ( 34 unt; 7 def)
% Number of atoms : 703 ( 397 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 522 ( 189 ~; 270 |; 50 &)
% ( 4 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 126 ( 0 sgn 96 !; 30 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X1,X2] :
( ( X2 = f(g(X2))
& X1 = f(g(X1)) )
=> X1 = X2 )
& ? [X0] : X0 = f(g(X0)) )
<=> ( ! [X1,X2] :
( ( X2 = g(f(X2))
& X1 = g(f(X1)) )
=> X1 = X2 )
& ? [X0] : X0 = g(f(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_cute_thing) ).
fof(f2,negated_conjecture,
~ ( ( ! [X1,X2] :
( ( X2 = f(g(X2))
& X1 = f(g(X1)) )
=> X1 = X2 )
& ? [X0] : X0 = f(g(X0)) )
<=> ( ! [X1,X2] :
( ( X2 = g(f(X2))
& X1 = g(f(X1)) )
=> X1 = X2 )
& ? [X0] : X0 = g(f(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ( ! [X1,X2] :
( ( X2 = f(g(X2))
& X1 = f(g(X1)) )
=> X1 = X2 )
& ? [X0] : X0 = f(g(X0)) )
<=> ( ! [X4,X5] :
( ( g(f(X5)) = X5
& g(f(X4)) = X4 )
=> X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ( ! [X1,X2] :
( f(g(X2)) != X2
| f(g(X1)) != X1
| X1 = X2 )
& ? [X0] : X0 = f(g(X0)) )
<~> ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X1,X2] :
( f(g(X2)) != X2
| f(g(X1)) != X1
| X1 = X2 )
& ? [X0] : X0 = f(g(X0)) )
<~> ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) ),
inference(flattening,[],[f4]) ).
fof(f12,plain,
( ( sP0
| ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) )
& ( ~ sP0
| ? [X4,X5] :
( g(f(X5)) = X5
& g(f(X4)) = X4
& X4 != X5 )
| ! [X3] : g(f(X3)) != X3 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f13,plain,
( ( sP0
| ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) )
& ( ~ sP0
| ? [X4,X5] :
( g(f(X5)) = X5
& g(f(X4)) = X4
& X4 != X5 )
| ! [X3] : g(f(X3)) != X3 ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( sP0
| ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) )
& ( ~ sP0
| ? [X1,X2] :
( g(f(X2)) = X2
& g(f(X1)) = X1
& X1 != X2 )
| ! [X0] : g(f(X0)) != X0 ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ( sP0
| ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& sK6 = g(f(sK6)) ) )
& ( ~ sP0
| ( sK5 = g(f(sK5))
& sK4 = g(f(sK4))
& sK4 != sK5 )
| ! [X0] : g(f(X0)) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f14]) ).
fof(f21,plain,
! [X4,X5] :
( sP0
| g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
( sP0
| sK6 = g(f(sK6)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0] :
( ~ sP0
| sK5 = g(f(sK5))
| g(f(X0)) != X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0] :
( ~ sP0
| sK4 = g(f(sK4))
| g(f(X0)) != X0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] :
( ~ sP0
| sK4 != sK5
| g(f(X0)) != X0 ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( ~ sP0
| ( sK4 != sK5 )
| ( g(f(X0)) != X0 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( ( g(f(sK4)) = sK4 )
| ~ sP0
| ( g(f(X0)) != X0 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( ( g(f(sK5)) = sK5 )
| ~ sP0
| ( g(f(X0)) != X0 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_57,negated_conjecture,
( sP0
| ( g(f(sK6)) = sK6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ( g(f(X1)) != X1 )
| ( g(f(X0)) != X0 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_620,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( g(f(X0)) != X0 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_56]) ).
tcf(c_621,negated_conjecture,
( iPr_def_10
| ( g(f(sK5)) = sK5 )
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_622,negated_conjecture,
( iPr_def_10
| ( g(f(sK4)) = sK4 )
| ~ sP0 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).
tcf(c_623,negated_conjecture,
( iPr_def_10
| ~ sP0
| ( sK4 != sK5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_54]) ).
tcf(c_628,definition,
iPr_def_12 = f(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_629,definition,
iPr_def_13 = g(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_630,definition,
iPr_def_14 = f(sK5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_631,definition,
iPr_def_15 = g(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_632,definition,
iPr_def_16 = f(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_633,definition,
iPr_def_17 = g(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_634,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0
| ( X0 = X1 )
| ( g(f(X1)) != X1 )
| ( g(f(X0)) != X0 ) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_635,negated_conjecture,
( sP0
| ( iPr_def_13 = sK6 ) ),
inference(demodulation,[status(thm)],[c_57,c_628,c_629]) ).
tcf(c_636,negated_conjecture,
( iPr_def_10
| ( iPr_def_15 = sK5 )
| ~ sP0 ),
inference(demodulation,[status(thm)],[c_621,c_630,c_631]) ).
tcf(c_638,negated_conjecture,
( iPr_def_10
| ( iPr_def_17 = sK4 )
| ~ sP0 ),
inference(demodulation,[status(thm)],[c_622,c_632,c_633]) ).
tcf(c_640,negated_conjecture,
( iPr_def_10
| ~ sP0
| ( sK4 != sK5 ) ),
inference(demodulation,[status(thm)],[c_623]) ).
tcf(c_641,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( g(f(X0)) != X0 ) ),
inference(demodulation,[status(thm)],[c_620]) ).
tcf(c_755,plain,
( iPr_def_10
| ( sK6 = iPr_def_13 )
| ( sK5 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_635,c_636]) ).
tcf(c_765,plain,
( iPr_def_10
| ( sK6 = iPr_def_13 )
| ( sK4 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_635,c_638]) ).
tcf(c_799,plain,
! [X0: $i] :
( sP0
| ( X0 = sK6 )
| ( g(iPr_def_12) != sK6 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_628,c_634]) ).
tcf(c_800,plain,
( ~ iPr_def_10
| ( g(iPr_def_12) != sK6 ) ),
inference(superposition,[status(thm)],[c_628,c_641]) ).
tcf(c_801,plain,
( ~ iPr_def_10
| ( sK6 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_800,c_629]) ).
tcf(c_804,plain,
! [X0: $i] :
( sP0
| ( X0 = sK6 )
| ( sK6 != iPr_def_13 )
| ( g(f(X0)) != X0 ) ),
inference(light_normalisation,[status(thm)],[c_799,c_629]) ).
tcf(c_810,plain,
! [X0: $i] :
( sP0
| ( X0 = sK5 )
| ( g(iPr_def_14) != sK5 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_630,c_634]) ).
tcf(c_815,plain,
! [X0: $i] :
( sP0
| ( X0 = sK5 )
| ( sK5 != iPr_def_15 )
| ( g(f(X0)) != X0 ) ),
inference(light_normalisation,[status(thm)],[c_810,c_631]) ).
tcf(c_859,plain,
( sP0
| ( sK5 = sK6 )
| ( sK6 != iPr_def_13 )
| ( g(iPr_def_14) != sK5 ) ),
inference(superposition,[status(thm)],[c_630,c_804]) ).
tcf(c_861,plain,
( sP0
| ( sK5 = sK6 )
| ( sK6 != iPr_def_13 )
| ( sK5 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_859,c_631]) ).
tcf(c_879,plain,
( sP0
| ( sK4 = sK5 )
| ( sK5 != iPr_def_15 )
| ( g(iPr_def_16) != sK4 ) ),
inference(superposition,[status(thm)],[c_632,c_815]) ).
tcf(c_883,plain,
( sP0
| ( sK4 = sK5 )
| ( sK5 != iPr_def_15 )
| ( sK4 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_879,c_633]) ).
fof(f6,definition,
( sP0
<=> ( ! [X1,X2] :
( f(g(X2)) != X2
| f(g(X1)) != X1
| X1 = X2 )
& ? [X0] : X0 = f(g(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP0
<~> ( ! [X4,X5] :
( g(f(X5)) != X5
| g(f(X4)) != X4
| X4 = X5 )
& ? [X3] : g(f(X3)) = X3 ) ),
inference(definition_folding,[],[f5,f6]) ).
fof(f8,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( f(g(X2)) != X2
| f(g(X1)) != X1
| X1 = X2 )
& ? [X0] : X0 = f(g(X0)) ) )
& ( ? [X1,X2] :
( f(g(X2)) = X2
& f(g(X1)) = X1
& X1 != X2 )
| ! [X0] : f(g(X0)) != X0
| sP0 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( ~ sP0
| ( ! [X1,X2] :
( f(g(X2)) != X2
| f(g(X1)) != X1
| X1 = X2 )
& ? [X0] : X0 = f(g(X0)) ) )
& ( ? [X1,X2] :
( f(g(X2)) = X2
& f(g(X1)) = X1
& X1 != X2 )
| ! [X0] : f(g(X0)) != X0
| sP0 ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
( ( ~ sP0
| ( ! [X4,X5] :
( f(g(X5)) != X5
| f(g(X4)) != X4
| X4 = X5 )
& ? [X3] : f(g(X3)) = X3 ) )
& ( ? [X1,X2] :
( f(g(X2)) = X2
& f(g(X1)) = X1
& X1 != X2 )
| ! [X0] : f(g(X0)) != X0
| sP0 ) ),
inference(rectify,[],[f9]) ).
fof(f11,plain,
( ( ~ sP0
| ( ! [X4,X5] :
( f(g(X5)) != X5
| f(g(X4)) != X4
| X4 = X5 )
& sK3 = f(g(sK3)) ) )
& ( ( sK2 = f(g(sK2))
& sK1 = f(g(sK1))
& sK1 != sK2 )
| ! [X0] : f(g(X0)) != X0
| sP0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f10]) ).
fof(f16,plain,
! [X4,X5] :
( ~ sP0
| f(g(X5)) != X5
| f(g(X4)) != X4
| X4 = X5 ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
( ~ sP0
| sK3 = f(g(sK3)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0] :
( sK2 = f(g(sK2))
| f(g(X0)) != X0
| sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X0] :
( sK1 = f(g(sK1))
| f(g(X0)) != X0
| sP0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X0] :
( sK1 != sK2
| f(g(X0)) != X0
| sP0 ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_49,plain,
! [X0: $i] :
( sP0
| ( sK1 != sK2 )
| ( f(g(X0)) != X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_50,plain,
! [X0: $i] :
( sP0
| ( f(g(sK1)) = sK1 )
| ( f(g(X0)) != X0 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,plain,
! [X0: $i] :
( sP0
| ( f(g(sK2)) = sK2 )
| ( f(g(X0)) != X0 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_52,plain,
( ( f(g(sK3)) = sK3 )
| ~ sP0 ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ sP0
| ( f(g(X1)) != X1 )
| ( f(g(X0)) != X0 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_624,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( f(g(X0)) != X0 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_51]) ).
tcf(c_625,plain,
( iPr_def_11
| sP0
| ( f(g(sK2)) = sK2 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_51]) ).
tcf(c_626,plain,
( iPr_def_11
| sP0
| ( f(g(sK1)) = sK1 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_50]) ).
tcf(c_627,plain,
( iPr_def_11
| sP0
| ( sK1 != sK2 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_49]) ).
tcf(c_929,plain,
( ( sK6 = iPr_def_13 )
| ( f(g(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_635,c_52]) ).
tcf(c_940,plain,
( ( sK6 = iPr_def_13 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_929,c_641]) ).
tcf(c_1042,plain,
( ~ iPr_def_11
| ( f(iPr_def_13) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_629,c_624]) ).
tcf(c_1044,plain,
( ~ iPr_def_11
| ( f(iPr_def_17) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_633,c_624]) ).
tcf(c_1061,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_940,c_801,c_940]) ).
tcf(c_1063,plain,
( ( sK6 = iPr_def_13 )
| ( sK4 = iPr_def_17 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_765,c_1061]) ).
tcf(c_1064,plain,
( ( sK6 = iPr_def_13 )
| ( sK5 = iPr_def_15 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_755,c_1061]) ).
tcf(c_1065,plain,
( ( sK4 = iPr_def_17 )
| ~ sP0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_638,c_1061]) ).
tcf(c_1066,plain,
( ( sK5 = iPr_def_15 )
| ~ sP0 ),
inference(backward_subsumption_resolution,[status(thm)],[c_636,c_1061]) ).
tcf(c_1067,plain,
( ~ sP0
| ( sK4 != sK5 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_640,c_1061]) ).
tcf(c_1086,plain,
( iPr_def_11
| ( sK4 = iPr_def_17 )
| ( f(g(sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_626,c_1065]) ).
tcf(c_1087,plain,
( iPr_def_11
| ( sK4 = iPr_def_17 )
| ( f(g(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_625,c_1065]) ).
tcf(c_1099,plain,
( iPr_def_11
| ( sK5 = iPr_def_15 )
| ( f(g(sK1)) = sK1 ) ),
inference(superposition,[status(thm)],[c_626,c_1066]) ).
tcf(c_1100,plain,
( iPr_def_11
| ( sK5 = iPr_def_15 )
| ( f(g(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_625,c_1066]) ).
tcf(c_1140,plain,
( ( sK4 = iPr_def_17 )
| ( f(iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1063,c_628]) ).
tcf(c_1148,plain,
( ( sK5 = iPr_def_15 )
| ( f(iPr_def_13) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_1064,c_628]) ).
tcf(c_1187,plain,
( ( sK4 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_1140,c_1042]) ).
tcf(c_1207,plain,
( ( sK5 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_1148,c_1042]) ).
tcf(c_1229,plain,
( ( f(g(sK1)) = sK1 )
| ( sK4 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_1086,c_1086,c_1187]) ).
tcf(c_1230,plain,
( ( sK4 = iPr_def_17 )
| ( f(g(sK1)) = sK1 ) ),
inference(renaming,[status(thm)],[c_1229]) ).
tcf(c_1241,plain,
! [X0: $i] :
( sP0
| ( sK4 = iPr_def_17 )
| ( g(sK1) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_1230,c_634]) ).
tcf(c_1265,plain,
( ( f(g(sK2)) = sK2 )
| ( sK4 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_1087,c_1087,c_1187]) ).
tcf(c_1266,plain,
( ( sK4 = iPr_def_17 )
| ( f(g(sK2)) = sK2 ) ),
inference(renaming,[status(thm)],[c_1265]) ).
tcf(c_1277,plain,
! [X0: $i] :
( sP0
| ( sK4 = iPr_def_17 )
| ( g(sK2) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_1266,c_634]) ).
tcf(c_1296,plain,
! [X0: $i] :
( ( g(f(X0)) != X0 )
| ( g(sK1) = X0 )
| ( sK4 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_1241,c_1065,c_1241]) ).
tcf(c_1297,plain,
! [X0: $i] :
( ( sK4 = iPr_def_17 )
| ( g(sK1) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(renaming,[status(thm)],[c_1296]) ).
tcf(c_1312,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK1) = iPr_def_13 )
| ( g(iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1140,c_1297]) ).
tcf(c_1315,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK1) = iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_1312,c_629]) ).
tcf(c_1333,plain,
! [X0: $i] :
( ( g(f(X0)) != X0 )
| ( g(sK2) = X0 )
| ( sK4 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_1277,c_1065,c_1277]) ).
tcf(c_1334,plain,
! [X0: $i] :
( ( sK4 = iPr_def_17 )
| ( g(sK2) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(renaming,[status(thm)],[c_1333]) ).
tcf(c_1347,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK2) = sK6 )
| ( g(iPr_def_12) != sK6 ) ),
inference(superposition,[status(thm)],[c_628,c_1334]) ).
tcf(c_1349,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK2) = iPr_def_13 )
| ( g(iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1140,c_1334]) ).
tcf(c_1350,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK2) = iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_1349,c_629]) ).
tcf(c_1353,plain,
( ( sK4 = iPr_def_17 )
| ( g(sK2) = sK6 )
| ( sK6 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_1347,c_629]) ).
tcf(c_1381,plain,
( ( f(g(sK1)) = sK1 )
| ( sK5 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1099,c_1099,c_1207]) ).
tcf(c_1382,plain,
( ( sK5 = iPr_def_15 )
| ( f(g(sK1)) = sK1 ) ),
inference(renaming,[status(thm)],[c_1381]) ).
tcf(c_1395,plain,
! [X0: $i] :
( sP0
| ( sK5 = iPr_def_15 )
| ( g(sK1) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_1382,c_634]) ).
tcf(c_1419,plain,
! [X0: $i] :
( ( g(f(X0)) != X0 )
| ( g(sK1) = X0 )
| ( sK5 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1395,c_1066,c_1395]) ).
tcf(c_1420,plain,
! [X0: $i] :
( ( sK5 = iPr_def_15 )
| ( g(sK1) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(renaming,[status(thm)],[c_1419]) ).
tcf(c_1435,plain,
( ( sK5 = iPr_def_15 )
| ( g(sK1) = iPr_def_13 )
| ( g(iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1148,c_1420]) ).
tcf(c_1437,plain,
( ( sK5 = iPr_def_15 )
| ( g(sK1) = iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_1435,c_629]) ).
tcf(c_1449,plain,
( ( f(g(sK2)) = sK2 )
| ( sK5 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1100,c_1100,c_1207]) ).
tcf(c_1450,plain,
( ( sK5 = iPr_def_15 )
| ( f(g(sK2)) = sK2 ) ),
inference(renaming,[status(thm)],[c_1449]) ).
tcf(c_1465,plain,
! [X0: $i] :
( sP0
| ( sK5 = iPr_def_15 )
| ( g(sK2) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_1450,c_634]) ).
tcf(c_1513,plain,
! [X0: $i] :
( ( g(f(X0)) != X0 )
| ( g(sK2) = X0 )
| ( sK5 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1465,c_1066,c_1465]) ).
tcf(c_1514,plain,
! [X0: $i] :
( ( sK5 = iPr_def_15 )
| ( g(sK2) = X0 )
| ( g(f(X0)) != X0 ) ),
inference(renaming,[status(thm)],[c_1513]) ).
tcf(c_1530,plain,
( ( sK5 = iPr_def_15 )
| ( g(sK2) = iPr_def_13 )
| ( g(iPr_def_12) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1148,c_1514]) ).
tcf(c_1532,plain,
( ( sK5 = iPr_def_15 )
| ( g(sK2) = iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_1530,c_629]) ).
tcf(c_1574,plain,
( ( sK4 = iPr_def_17 )
| ( f(iPr_def_13) = sK1 ) ),
inference(superposition,[status(thm)],[c_1315,c_1230]) ).
tcf(c_1715,plain,
( ( sK4 = iPr_def_17 )
| ( f(iPr_def_13) = sK2 ) ),
inference(superposition,[status(thm)],[c_1350,c_1266]) ).
tcf(c_1731,plain,
( ( sK5 = iPr_def_15 )
| ( f(iPr_def_13) = sK1 ) ),
inference(superposition,[status(thm)],[c_1437,c_1382]) ).
tcf(c_1749,plain,
( ( sK5 = iPr_def_15 )
| ( f(iPr_def_13) = sK2 ) ),
inference(superposition,[status(thm)],[c_1532,c_1450]) ).
tcf(c_1956,plain,
( ( sK4 = iPr_def_17 )
| ( sK1 = sK2 ) ),
inference(superposition,[status(thm)],[c_1715,c_1574]) ).
tcf(c_1969,plain,
sK4 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_1353,c_627,c_1065,c_1187,c_1956]) ).
tcf(c_1987,plain,
( ~ sP0
| ( sK5 != iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1067,c_1969]) ).
tcf(c_1989,plain,
( sP0
| ( sK5 = iPr_def_17 )
| ( iPr_def_17 != iPr_def_17 )
| ( sK5 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_883,c_1969]) ).
tcf(c_1992,plain,
f(iPr_def_17) = iPr_def_16,
inference(demodulation,[status(thm)],[c_632,c_1969]) ).
tcf(c_2002,plain,
( sP0
| ( sK5 = iPr_def_17 )
| ( sK5 != iPr_def_15 ) ),
inference(equality_resolution_simp,[status(thm)],[c_1989]) ).
tcf(c_2010,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_1044,c_1992]) ).
tcf(c_2013,plain,
( sP0
| ( sK1 != sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_627,c_2010]) ).
tcf(c_2014,plain,
( sP0
| ( f(g(sK1)) = sK1 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_626,c_2010]) ).
tcf(c_2015,plain,
( sP0
| ( f(g(sK2)) = sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_625,c_2010]) ).
tcf(c_2104,plain,
! [X0: $i] :
( sP0
| ( sK5 = iPr_def_15 )
| ( X0 = iPr_def_13 )
| ( g(sK2) != iPr_def_13 )
| ( g(f(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_1749,c_634]) ).
tcf(c_2105,plain,
( ( sK5 = iPr_def_15 )
| ( sK1 = sK2 ) ),
inference(superposition,[status(thm)],[c_1749,c_1731]) ).
tcf(c_2116,plain,
sK5 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_2104,c_627,c_1066,c_2010,c_2105]) ).
tcf(c_2120,plain,
( ~ sP0
| ( iPr_def_15 != iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1987,c_2116]) ).
tcf(c_2132,plain,
( sP0
| ( sK6 = iPr_def_15 )
| ( iPr_def_15 != iPr_def_15 )
| ( sK6 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_861,c_2116]) ).
tcf(c_2134,plain,
f(iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_630,c_2116]) ).
tcf(c_2140,plain,
( sP0
| ( sK6 = iPr_def_15 )
| ( sK6 != iPr_def_13 ) ),
inference(equality_resolution_simp,[status(thm)],[c_2132]) ).
tcf(c_2264,plain,
( sP0
| ( sK5 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_2002,c_627,c_1066,c_2010,c_2002,c_2105]) ).
tcf(c_2266,plain,
( sP0
| ( iPr_def_15 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2264,c_2116]) ).
tcf(c_2273,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( f(g(sK3)) = sK3 ) ),
inference(superposition,[status(thm)],[c_2266,c_52]) ).
tcf(c_2281,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_17 )
| ( X0 = sK3 )
| ~ sP0
| ( f(g(X0)) != X0 ) ),
inference(superposition,[status(thm)],[c_2273,c_53]) ).
tcf(c_3059,plain,
! [X0: $i] :
( ( f(g(X0)) != X0 )
| ~ sP0
| ( X0 = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_2281,c_2120,c_2281]) ).
tcf(c_3060,plain,
! [X0: $i] :
( ( X0 = sK3 )
| ~ sP0
| ( f(g(X0)) != X0 ) ),
inference(renaming,[status(thm)],[c_3059]) ).
tcf(c_3079,plain,
( ( sK3 = iPr_def_14 )
| ~ sP0
| ( f(iPr_def_15) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_631,c_3060]) ).
tcf(c_3080,plain,
( ( sK3 = iPr_def_16 )
| ~ sP0
| ( f(iPr_def_17) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_633,c_3060]) ).
tcf(c_3081,plain,
( ( sK3 = iPr_def_16 )
| ~ sP0 ),
inference(ground_joinability,[status(thm)],[c_3080,c_1992]) ).
tcf(c_3084,plain,
( ( sK3 = iPr_def_14 )
| ~ sP0 ),
inference(ground_joinability,[status(thm)],[c_3079,c_2134]) ).
tcf(c_3119,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sK3 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_2266,c_3084]) ).
tcf(c_3233,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sK3 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_2266,c_3081]) ).
tcf(c_3427,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_3233,c_3119]) ).
tcf(c_3634,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( f(iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_3427,c_1992]) ).
tcf(c_3637,plain,
iPr_def_14 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_3634,c_2134]) ).
tcf(c_3651,plain,
g(iPr_def_14) = iPr_def_17,
inference(demodulation,[status(thm)],[c_633,c_3637]) ).
tcf(c_3652,plain,
iPr_def_15 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_3651,c_631]) ).
tcf(c_3653,plain,
~ sP0,
inference(backward_subsumption_resolution,[status(thm)],[c_2120,c_3652]) ).
tcf(c_3668,plain,
( ( sK6 = iPr_def_15 )
| ( sK6 != iPr_def_13 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2140,c_3653]) ).
tcf(c_3670,plain,
f(g(sK2)) = sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_2015,c_3653]) ).
tcf(c_3671,plain,
f(g(sK1)) = sK1,
inference(backward_subsumption_resolution,[status(thm)],[c_2014,c_3653]) ).
tcf(c_3672,plain,
sK1 != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_2013,c_3653]) ).
tcf(c_3674,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ( sK6 != iPr_def_13 )
| ( g(f(X0)) != X0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_804,c_3653]) ).
tcf(c_3675,plain,
sK6 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_635,c_3653]) ).
tcf(c_3694,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ( g(f(X0)) != X0 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3674,c_3675]) ).
tcf(c_3695,plain,
sK6 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_3668,c_3675]) ).
tcf(c_3700,plain,
f(iPr_def_15) = iPr_def_12,
inference(demodulation,[status(thm)],[c_628,c_3695]) ).
tcf(c_3701,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_2134,c_3700]) ).
tcf(c_3705,plain,
g(iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_631,c_3701]) ).
tcf(c_3706,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_3705,c_629]) ).
tcf(c_3723,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( g(f(X0)) != X0 ) ),
inference(light_normalisation,[status(thm)],[c_3694,c_3675]) ).
tcf(c_3731,plain,
f(iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3700,c_3706]) ).
tcf(c_3748,plain,
g(sK2) = iPr_def_13,
inference(superposition,[status(thm)],[c_3670,c_3723]) ).
tcf(c_3752,plain,
f(iPr_def_13) = sK2,
inference(demodulation,[status(thm)],[c_3670,c_3748]) ).
tcf(c_3753,plain,
sK2 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3752,c_3731]) ).
tcf(c_3754,plain,
sK1 != iPr_def_12,
inference(demodulation,[status(thm)],[c_3672,c_3753]) ).
tcf(c_3758,plain,
g(sK1) = iPr_def_13,
inference(superposition,[status(thm)],[c_3671,c_3723]) ).
tcf(c_3762,plain,
f(iPr_def_13) = sK1,
inference(demodulation,[status(thm)],[c_3671,c_3758]) ).
tcf(c_3763,plain,
sK1 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3762,c_3731]) ).
tcf(c_3764,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3763,c_3754]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN551+1 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.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 01:47:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 1.67/1.07 % SZS status Started for theBenchmark.p
% 1.67/1.07 % SZS status Theorem for theBenchmark.p
% 1.67/1.07
% 1.67/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.67/1.07
% 1.67/1.07 % ------ iProver source info
% 1.67/1.07
% 1.67/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 1.67/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.67/1.07 % git: non_committed_changes: false
% 1.67/1.07
% 1.67/1.07 % ------ Parsing...
% 1.67/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.67/1.07
% 1.67/1.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.67/1.07
% 1.67/1.07 % ------ Preprocessing... gs_s sp: 6 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.67/1.07
% 1.67/1.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.67/1.07 % ------ Proving...
% 1.67/1.07 % ------ Problem Properties
% 1.67/1.07
% 1.67/1.07 %
% 1.67/1.07 % clauses 18
% 1.67/1.07 % conjectures 6
% 1.67/1.07 % EPR 5
% 1.67/1.07 % Horn 11
% 1.67/1.07 % unary 6
% 1.67/1.07 % binary 4
% 1.67/1.07 % lits 40
% 1.67/1.07 % lits eq 22
% 1.67/1.07 % fd_pure 0
% 1.67/1.07 % fd_pseudo 0
% 1.67/1.07 % fd_cond 0
% 1.67/1.07 % fd_pseudo_cond 2
% 1.67/1.07 % AC symbols 0
% 1.67/1.07
% 1.67/1.07 % ------ Schedule dynamic 5 is on
% 1.67/1.07
% 1.67/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.67/1.07
% 1.67/1.07
% 1.67/1.07 % ------
% 1.67/1.07 % Current options:
% 1.67/1.07 % ------
% 1.67/1.07
% 1.67/1.07
% 1.67/1.07 %
% 1.67/1.07
% 1.67/1.07 % ------ Proving...
% 1.67/1.07 %
% 1.67/1.07
% 1.67/1.07 % SZS status Theorem for theBenchmark.p
% 1.67/1.07
% 1.67/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.67/1.07
%------------------------------------------------------------------------------