%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 03:51:32 PM UTC 2026
% Result : Theorem 2.26s 6.33s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 107 ( 8 unt; 0 def)
% Number of atoms : 396 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 460 ( 171 ~; 236 |; 50 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 242 ( 0 sgn 200 !; 42 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [X0] :
! [X1] : g_true_only(X0,X1)
& ? [X0] :
( ~ ? [X1] : g_false_only(X0,X1)
& ? [X1] : g_both(X0,X1) )
& ~ ? [X0] :
( ? [X1] : g_false_only(X0,X1)
& g_false_only(a,X0) )
& ? [X0] :
( ~ ! [X1] : g_true_only(X0,X1)
& ~ g_true_only(a,X0)
& ( ( ~ ? [X1] : g_false_only(X0,X1)
& ? [X1] : g_both(X0,X1) )
| g_both(a,X0) ) ) )
| ? [X0] :
! [X1] : g_true_only(X0,X1)
| ? [X0] :
( ? [X1] : g_false_only(X0,X1)
& g_false_only(a,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc6) ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [X0] :
! [X1] : g_true_only(X0,X1)
& ? [X0] :
( ~ ? [X1] : g_false_only(X0,X1)
& ? [X1] : g_both(X0,X1) )
& ~ ? [X0] :
( ? [X1] : g_false_only(X0,X1)
& g_false_only(a,X0) )
& ? [X0] :
( ~ ! [X1] : g_true_only(X0,X1)
& ~ g_true_only(a,X0)
& ( ( ~ ? [X1] : g_false_only(X0,X1)
& ? [X1] : g_both(X0,X1) )
| g_both(a,X0) ) ) )
| ? [X0] :
! [X1] : g_true_only(X0,X1)
| ? [X0] :
( ? [X1] : g_false_only(X0,X1)
& g_false_only(a,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( ~ g_false(X0,X1)
& g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
fof(f4,axiom,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_false(X0,X1)
& g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
fof(f5,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( ~ g_true(X0,X1)
& g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
fof(f6,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ( ~ ? [X13] :
! [X14] : g_true_only(X13,X14)
& ? [X10] :
( ~ ? [X12] : g_false_only(X10,X12)
& ? [X11] : g_both(X10,X11) )
& ~ ? [X8] :
( ? [X9] : g_false_only(X8,X9)
& g_false_only(a,X8) )
& ? [X4] :
( ~ ! [X7] : g_true_only(X4,X7)
& ~ g_true_only(a,X4)
& ( ( ~ ? [X6] : g_false_only(X4,X6)
& ? [X5] : g_both(X4,X5) )
| g_both(a,X4) ) ) )
| ? [X2] :
! [X3] : g_true_only(X2,X3)
| ? [X0] :
( ? [X1] : g_false_only(X0,X1)
& g_false_only(a,X0) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ( ? [X13] :
! [X14] : g_true_only(X13,X14)
| ! [X10] :
( ? [X12] : g_false_only(X10,X12)
| ! [X11] : ~ g_both(X10,X11) )
| ? [X8] :
( ? [X9] : g_false_only(X8,X9)
& g_false_only(a,X8) )
| ! [X4] :
( ! [X7] : g_true_only(X4,X7)
| g_true_only(a,X4)
| ( ( ? [X6] : g_false_only(X4,X6)
| ! [X5] : ~ g_both(X4,X5) )
& ~ g_both(a,X4) ) ) )
& ! [X2] :
? [X3] : ~ g_true_only(X2,X3)
& ! [X0] :
( ! [X1] : ~ g_false_only(X0,X1)
| ~ g_false_only(a,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( ( ! [X14] : g_true_only(sK5,X14)
| ! [X10] :
( g_false_only(X10,sK4(X10))
| ! [X11] : ~ g_both(X10,X11) )
| ( g_false_only(sK2,sK3)
& g_false_only(a,sK2) )
| ! [X4] :
( ! [X7] : g_true_only(X4,X7)
| g_true_only(a,X4)
| ( ( g_false_only(X4,sK1(X4))
| ! [X5] : ~ g_both(X4,X5) )
& ~ g_both(a,X4) ) ) )
& ! [X2] : ~ g_true_only(X2,sK0(X2))
& ! [X0] :
( ! [X1] : ~ g_false_only(X0,X1)
| ~ g_false_only(a,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK0(X2)),skolemize(X6,sK1(X4)),skolemize(X8,sK2),skolemize(X9,sK3),skolemize(X12,sK4(X10)),skolemize(X13,sK5)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ( ~ g_true_only(X0,X1)
| ( ~ g_false(X0,X1)
& g_true(X0,X1) ) )
& ( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1] :
( ( ~ g_true_only(X0,X1)
| ( ~ g_false(X0,X1)
& g_true(X0,X1) ) )
& ( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( ~ g_both(X0,X1)
| ( g_false(X0,X1)
& g_true(X0,X1) ) )
& ( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ g_both(X0,X1)
| ( g_false(X0,X1)
& g_true(X0,X1) ) )
& ( ~ g_false(X0,X1)
| ~ g_true(X0,X1)
| g_both(X0,X1) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( ~ g_false_only(X0,X1)
| ( ~ g_true(X0,X1)
& g_false(X0,X1) ) )
& ( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ g_false_only(X0,X1)
| ( ~ g_true(X0,X1)
& g_false(X0,X1) ) )
& ( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X10,X11,X7,X14,X4,X5] :
( g_true_only(sK5,X14)
| g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| g_false_only(sK2,sK3)
| g_true_only(X4,X7)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4))
| ~ g_both(X4,X5) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X10,X11,X7,X14,X4,X5] :
( g_true_only(sK5,X14)
| g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| g_false_only(a,sK2)
| g_true_only(X4,X7)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4))
| ~ g_both(X4,X5) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X10,X11,X7,X14,X4] :
( g_true_only(sK5,X14)
| g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| g_false_only(sK2,sK3)
| g_true_only(X4,X7)
| g_true_only(a,X4)
| ~ g_both(a,X4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X10,X11,X7,X14,X4] :
( g_true_only(sK5,X14)
| g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| g_false_only(a,sK2)
| g_true_only(X4,X7)
| g_true_only(a,X4)
| ~ g_both(a,X4) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X2] : ~ g_true_only(X2,sK0(X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_false_only(a,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_false(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ g_false_only(a,X0)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] : ~ g_true_only(X0,sK0(X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( g_false_only(a,sK2)
| g_true_only(sK5,X4)
| g_true_only(a,X2)
| g_true_only(X2,X3)
| g_false_only(X0,sK4(X0))
| ~ g_both(a,X2)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( g_false_only(sK2,sK3)
| g_true_only(sK5,X4)
| g_true_only(a,X2)
| g_true_only(X2,X3)
| g_false_only(X0,sK4(X0))
| ~ g_both(a,X2)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( g_false_only(a,sK2)
| g_true_only(sK5,X5)
| g_true_only(a,X0)
| g_true_only(X0,X4)
| g_false_only(X2,sK4(X2))
| g_false_only(X0,sK1(X0))
| ~ g_both(X2,X3)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( g_false_only(sK2,sK3)
| g_true_only(sK5,X5)
| g_true_only(a,X0)
| g_true_only(X0,X4)
| g_false_only(X2,sK4(X2))
| g_false_only(X0,sK1(X0))
| ~ g_both(X2,X3)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| g_false_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_65,plain,
~ g_true_only(a,sK0(a)),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| g_false_only(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_59,c_56,c_64]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_62,c_59,c_56,c_64,c_55]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(renaming,[status(thm)],[c_84]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( g_true_only(X0,X1)
| g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_81]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(renaming,[status(thm)],[c_90]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_false_only(a,X0) ),
inference(prop_impl_just,[status(thm)],[c_49,c_78]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| ~ g_false(X0,X1)
| ~ g_true(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_64,c_89,c_85]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(resolution,[status(thm)],[c_91,c_137]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( ~ g_both(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[c_96,c_89]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( g_false_only(a,sK2)
| g_true_only(sK5,X4)
| g_true_only(X2,X3)
| g_false_only(X0,sK4(X0))
| ~ g_both(a,X2)
| ~ g_both(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_260]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( g_false_only(sK2,sK3)
| g_true_only(sK5,X4)
| g_true_only(X2,X3)
| g_false_only(X0,sK4(X0))
| ~ g_both(a,X2)
| ~ g_both(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_260]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| ~ g_false_only(a,X0) ),
inference(resolution,[status(thm)],[c_92,c_247]) ).
tcf(c_419,plain,
! [X0: $i] :
( ~ iPr_def_10
| g_true_only(sK5,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_275]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| g_true_only(X0,X1)
| ~ g_both(a,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_275]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| g_false_only(X0,sK4(X0))
| ~ g_both(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_275]) ).
tcf(c_422,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| g_false_only(sK2,sK3) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_275]) ).
tcf(c_423,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| g_false_only(a,sK2) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_274]) ).
tcf(c_424,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_13
| g_false_only(X0,sK1(X0))
| g_true_only(a,X0)
| g_true_only(X0,X2)
| ~ g_both(X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_54]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| g_false_only(sK2,sK3) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_54]) ).
tcf(c_426,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| g_false_only(a,sK2) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_53]) ).
tcf(c_427,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| g_false_only(sK2,sK3) ),
inference(demodulation,[status(thm)],[c_422]) ).
tcf(c_431,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| g_false_only(a,sK2) ),
inference(demodulation,[status(thm)],[c_423]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( g_true_only(X0,X1)
| ~ iPr_def_11
| ~ g_both(a,X0) ),
inference(demodulation,[status(thm)],[c_420]) ).
tcf(c_435,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| g_false_only(sK2,sK3) ),
inference(demodulation,[status(thm)],[c_425]) ).
tcf(c_439,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| g_false_only(a,sK2) ),
inference(demodulation,[status(thm)],[c_426]) ).
tcf(c_440,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( g_true_only(a,X0)
| g_true_only(X0,X2)
| g_false_only(X0,sK1(X0))
| ~ iPr_def_13
| ~ g_both(X0,X1) ),
inference(demodulation,[status(thm)],[c_424]) ).
tcf(c_441,plain,
! [X0: $i] :
( g_true_only(sK5,X0)
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_419]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,sK4(X0))
| ~ iPr_def_12
| ~ g_both(X0,X1) ),
inference(demodulation,[status(thm)],[c_421]) ).
tcf(c_443,negated_conjecture,
! [X0: $i] : ~ g_true_only(X0,sK0(X0)),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_444,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ g_false_only(a,X0)
| ~ g_false_only(X0,X1) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_449,plain,
! [X0: $i] :
( g_both(X0,sK0(X0))
| g_true_only(X0,sK0(X0))
| ~ g_false_only(a,X0) ),
inference(instantiation,[status(thm)],[c_277]) ).
tcf(c_450,plain,
! [X0: $i] :
( g_both(X0,sK0(X0))
| g_true_only(X0,sK0(X0))
| g_false_only(X0,sK0(X0)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_451,plain,
( g_both(a,sK0(a))
| g_true_only(a,sK0(a))
| g_false_only(a,sK0(a)) ),
inference(instantiation,[status(thm)],[c_450]) ).
tcf(c_453,plain,
! [X0: $i] :
( g_false_only(X0,sK4(X0))
| ~ iPr_def_12
| ~ g_both(X0,sK0(X0)) ),
inference(instantiation,[status(thm)],[c_442]) ).
tcf(c_454,plain,
( g_false_only(a,sK4(a))
| ~ iPr_def_12
| ~ g_both(a,sK0(a)) ),
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_456,plain,
! [X0: $i] :
( ~ g_false_only(a,sK0(a))
| ~ g_false_only(sK0(a),X0) ),
inference(instantiation,[status(thm)],[c_444]) ).
tcf(c_468,plain,
( g_both(sK0(a),sK0(sK0(a)))
| g_true_only(sK0(a),sK0(sK0(a)))
| ~ g_false_only(a,sK0(a)) ),
inference(instantiation,[status(thm)],[c_449]) ).
tcf(c_470,plain,
~ g_true_only(sK0(a),sK0(sK0(a))),
inference(instantiation,[status(thm)],[c_443]) ).
tcf(c_477,plain,
( g_false_only(sK0(a),sK4(sK0(a)))
| ~ iPr_def_12
| ~ g_both(sK0(a),sK0(sK0(a))) ),
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_485,plain,
( ~ g_false_only(a,sK0(a))
| ~ g_false_only(sK0(a),sK4(sK0(a))) ),
inference(instantiation,[status(thm)],[c_456]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i] :
( g_true_only(a,sK0(a))
| g_true_only(sK0(a),X1)
| g_false_only(sK0(a),sK1(sK0(a)))
| ~ iPr_def_13
| ~ g_both(sK0(a),X0) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_489,plain,
! [X0: $i] :
( g_true_only(X0,sK0(X0))
| ~ iPr_def_11
| ~ g_both(a,X0) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_496,plain,
! [X0: $i] :
( g_true_only(a,sK0(a))
| g_true_only(sK0(a),X0)
| g_false_only(sK0(a),sK1(sK0(a)))
| ~ iPr_def_13
| ~ g_both(sK0(a),sK0(sK0(a))) ),
inference(instantiation,[status(thm)],[c_486]) ).
tcf(c_500,plain,
( g_true_only(a,sK0(a))
| g_true_only(sK0(a),sK0(sK0(a)))
| g_false_only(sK0(a),sK1(sK0(a)))
| ~ iPr_def_13
| ~ g_both(sK0(a),sK0(sK0(a))) ),
inference(instantiation,[status(thm)],[c_496]) ).
tcf(c_503,plain,
( ~ g_false_only(a,sK0(a))
| ~ g_false_only(sK0(a),sK1(sK0(a))) ),
inference(instantiation,[status(thm)],[c_456]) ).
tcf(c_506,plain,
( g_true_only(sK0(a),sK0(sK0(a)))
| ~ iPr_def_11
| ~ g_both(a,sK0(a)) ),
inference(instantiation,[status(thm)],[c_489]) ).
tcf(c_518,plain,
! [X0: $i] :
( ~ g_false_only(a,sK2)
| ~ g_false_only(sK2,X0) ),
inference(instantiation,[status(thm)],[c_444]) ).
tcf(c_528,plain,
( ~ g_false_only(sK2,sK3)
| ~ g_false_only(a,sK2) ),
inference(instantiation,[status(thm)],[c_518]) ).
tcf(c_541,plain,
( g_true_only(sK5,sK0(sK5))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_441]) ).
tcf(c_542,plain,
~ g_true_only(sK5,sK0(sK5)),
inference(instantiation,[status(thm)],[c_443]) ).
tcf(c_558,plain,
( g_both(sK4(a),sK0(sK4(a)))
| g_true_only(sK4(a),sK0(sK4(a)))
| ~ g_false_only(a,sK4(a)) ),
inference(instantiation,[status(thm)],[c_449]) ).
tcf(c_559,plain,
! [X0: $i] :
( ~ g_false_only(a,sK4(a))
| ~ g_false_only(sK4(a),X0) ),
inference(instantiation,[status(thm)],[c_444]) ).
tcf(c_583,plain,
( ~ g_false_only(a,sK4(a))
| ~ g_false_only(sK4(a),sK4(sK4(a))) ),
inference(instantiation,[status(thm)],[c_559]) ).
tcf(c_584,plain,
( g_false_only(sK4(a),sK4(sK4(a)))
| ~ iPr_def_12
| ~ g_both(sK4(a),sK0(sK4(a))) ),
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_585,negated_conjecture,
( iPr_def_13
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_435,c_65,c_427,c_431,c_435,c_439,c_451,c_468,c_470,c_500,c_503,c_506,c_528,c_541,c_542]) ).
tcf(c_593,plain,
~ g_true_only(sK4(a),sK0(sK4(a))),
inference(instantiation,[status(thm)],[c_443]) ).
tcf(c_594,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_593,c_585,c_584,c_583,c_558,c_542,c_541,c_528,c_506,c_503,c_500,c_485,c_477,c_470,c_468,c_454,c_451,c_431,c_427,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.41 % Computer : n004.cluster.edu
% 0.11/5.41 % Model : x86_64 x86_64
% 0.11/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.41 % Memory : 8046.5625MB
% 0.11/5.41 % OS : Linux 6.8.0-71-generic
% 0.11/5.41 % CPULimit : 300
% 0.11/5.41 % WCLimit : 300
% 0.11/5.41 % DateTime : Fri Sep 25 03:13:55 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.45 Running first-order theorem proving
% 0.11/5.45 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
% 0.11/5.46
% 0.11/5.46 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.46
% 0.11/5.46 % Detected problem language: tptp
% 0.11/5.48 % Proving...
% 2.26/6.33 % SZS status Started for theBenchmark.p
% 2.26/6.33 % SZS status Theorem for theBenchmark.p
% 2.26/6.33
% 2.26/6.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.26/6.33
% 2.26/6.33 % ------ iProver source info
% 2.26/6.33
% 2.26/6.33 % git: date: 2026-07-19 20:42:38 +0200
% 2.26/6.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.26/6.33 % git: non_committed_changes: false
% 2.26/6.33
% 2.26/6.33 % ------ Parsing...
% 2.26/6.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.26/6.33
% 2.26/6.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.26/6.33
% 2.26/6.33 % ------ Preprocessing... gs_s sp: 12 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.26/6.33 % ------ Proving...
% 2.26/6.33 % ------ Problem Properties
% 2.26/6.33
% 2.26/6.33 %
% 2.26/6.33 % clauses 15
% 2.26/6.33 % conjectures 5
% 2.26/6.33 % EPR 12
% 2.26/6.33 % Horn 8
% 2.26/6.33 % unary 1
% 2.26/6.33 % binary 5
% 2.26/6.33 % lits 44
% 2.26/6.33 % lits eq 0
% 2.26/6.33 % fd_pure 0
% 2.26/6.33 % fd_pseudo 0
% 2.26/6.33 % fd_cond 0
% 2.26/6.33 % fd_pseudo_cond 0
% 2.26/6.33 % AC symbols 0
% 2.26/6.33
% 2.26/6.33 % ------ Schedule dynamic 5 is on
% 2.26/6.33
% 2.26/6.33 % ------ no equalities: superposition off
% 2.26/6.33
% 2.26/6.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/6.33
% 2.26/6.33
% 2.26/6.33 % ------
% 2.26/6.33 % Current options:
% 2.26/6.33 % ------
% 2.26/6.33
% 2.26/6.33
% 2.26/6.33 %
% 2.26/6.33
% 2.26/6.33 % ------ Proving...
% 2.26/6.33 %
% 2.26/6.33
% 2.26/6.33 % SZS status Theorem for theBenchmark.p
% 2.26/6.33
% 2.26/6.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/6.33
% 2.26/6.33
%------------------------------------------------------------------------------