%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV515+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 : n001.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 03:02:20 PM UTC 2026
% Result : Theorem 2.48s 1.33s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f53ERROR: Could not build tree for root c_507ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc1) ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X1)
& g_false_only(X1,X0) )
| ( g_false_only(X1,X1)
& g_true_only(X1,X0) ) )
& ? [X0] :
( ~ ? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) )
& ? [X1] :
( g_both(X1,X1)
& g_both(X1,X0) ) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,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,
~ ( ( ~ ? [X5] :
! [X6] :
( ( g_true_only(X6,X6)
& g_false_only(X6,X5) )
| ( g_false_only(X6,X6)
& g_true_only(X6,X5) ) )
& ? [X2] :
( ~ ? [X4] :
( ( ( g_both(X4,X4)
| g_false_only(X4,X4) )
& g_false_only(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_false_only(X4,X4) )
& g_both(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_both(X4,X4) )
& g_true_only(X4,X2) ) )
& ? [X3] :
( g_both(X3,X3)
& g_both(X3,X2) ) ) )
| ! [X0] :
? [X1] :
( ( ( g_both(X1,X1)
| g_false_only(X1,X1) )
& g_false_only(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_false_only(X1,X1) )
& g_both(X1,X0) )
| ( ( g_true_only(X1,X1)
| g_both(X1,X1) )
& g_true_only(X1,X0) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ( ? [X5] :
! [X6] :
( ( g_true_only(X6,X6)
& g_false_only(X6,X5) )
| ( g_false_only(X6,X6)
& g_true_only(X6,X5) ) )
| ! [X2] :
( ? [X4] :
( ( ( g_both(X4,X4)
| g_false_only(X4,X4) )
& g_false_only(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_false_only(X4,X4) )
& g_both(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_both(X4,X4) )
& g_true_only(X4,X2) ) )
| ! [X3] :
( ~ g_both(X3,X3)
| ~ g_both(X3,X2) ) ) )
& ? [X0] :
! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,X0) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( ( ? [X2] :
! [X3] :
( ( g_true_only(X3,X3)
& g_false_only(X3,X2) )
| ( g_false_only(X3,X3)
& g_true_only(X3,X2) ) )
| sP0 )
& ? [X0] :
! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( ( ! [X3] :
( ( g_true_only(X3,X3)
& g_false_only(X3,sK3) )
| ( g_false_only(X3,X3)
& g_true_only(X3,sK3) ) )
| sP0 )
& ! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,sK2) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,sK2) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X2,sK3)],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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(f19,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,[],[f18]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f30,plain,
! [X3] :
( g_true_only(X3,X3)
| g_false_only(X3,X3)
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X1] :
( ~ g_both(X1,X1)
| ~ g_false_only(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| ~ g_false_only(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X1] :
( ~ g_true_only(X1,X1)
| ~ g_both(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| ~ g_both(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X1] :
( ~ g_true_only(X1,X1)
| ~ g_true_only(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X1] :
( ~ g_both(X1,X1)
| ~ g_true_only(X1,sK2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f42,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_true(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f47,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),sK1(X1))
| g_true_only(sK1(X1),sK1(X1))
| g_both(sK1(X1),sK1(X1))
| ~ sP0
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( ~ g_true_only(X0,sK2)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ~ g_true_only(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK2)
| ~ g_false_only(X0,X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK2)
| ~ g_false_only(X0,X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK2)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] :
( sP0
| g_false_only(X0,X0)
| g_true_only(X0,X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( g_false_only(X0,X1)
| g_true_only(X0,X1)
| g_both(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_77,plain,
( sP0
| g_false_only(sK2,sK2)
| g_true_only(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_86,plain,
~ g_false_only(sK2,sK2),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_88,plain,
~ g_true_only(sK2,sK2),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_89,plain,
( g_false_only(sK2,sK2)
| g_true_only(sK2,sK2)
| g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_94,plain,
( g_false_only(sK1(sK2),sK1(sK2))
| g_true_only(sK1(sK2),sK1(sK2))
| g_both(sK1(sK2),sK1(sK2))
| ~ sP0
| ~ g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_74,c_72,c_76]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( ~ g_true_only(X0,X1)
| ~ g_false(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_69]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(renaming,[status(thm)],[c_136]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ~ g_false_only(X0,X1)
| ~ g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(renaming,[status(thm)],[c_140]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| g_true(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_68,c_112]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[c_174,c_141]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] :
( ~ g_false_only(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[c_325,c_137]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( ~ g_true_only(X0,X1)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[c_146,c_137]) ).
tcf(c_472,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK2)
| ~ g_both(X0,X0) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ g_false_only(X0,sK2)
| ~ g_false_only(X0,X0) ),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ g_both(X0,sK2)
| ~ g_false_only(X0,X0) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ g_true_only(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_477,negated_conjecture,
! [X0: $i] :
( ~ g_true_only(X0,sK2)
| ~ g_both(X0,X0) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_479,plain,
( ~ g_true_only(sK1(sK2),sK2)
| ~ g_both(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_477]) ).
tcf(c_480,plain,
( ~ g_true_only(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_476]) ).
tcf(c_490,plain,
( ~ g_false_only(sK1(sK2),sK2)
| ~ g_false_only(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_473]) ).
tcf(c_491,plain,
( ~ g_false_only(sK1(sK2),sK2)
| ~ g_both(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_472]) ).
tcf(c_497,plain,
( ~ g_both(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_474]) ).
tcf(c_498,plain,
( ~ g_true_only(sK1(sK2),sK1(sK2))
| ~ g_both(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_380]) ).
tcf(c_499,plain,
( ~ g_false_only(sK1(sK2),sK1(sK2))
| ~ g_true_only(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_372]) ).
tcf(c_503,plain,
( ~ g_both(sK1(sK2),sK2)
| ~ g_false_only(sK1(sK2),sK1(sK2)) ),
inference(instantiation,[status(thm)],[c_475]) ).
fof(f9,definition,
( ~ sP0
| ! [X2] :
( ? [X4] :
( ( ( g_both(X4,X4)
| g_false_only(X4,X4) )
& g_false_only(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_false_only(X4,X4) )
& g_both(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_both(X4,X4) )
& g_true_only(X4,X2) ) )
| ! [X3] :
( ~ g_both(X3,X3)
| ~ g_both(X3,X2) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
( ( ? [X5] :
! [X6] :
( ( g_true_only(X6,X6)
& g_false_only(X6,X5) )
| ( g_false_only(X6,X6)
& g_true_only(X6,X5) ) )
| sP0 )
& ? [X0] :
! [X1] :
( ( ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_false_only(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) )
| ~ g_both(X1,X0) )
& ( ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) )
| ~ g_true_only(X1,X0) ) ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
( ~ sP0
| ! [X2] :
( ? [X4] :
( ( ( g_both(X4,X4)
| g_false_only(X4,X4) )
& g_false_only(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_false_only(X4,X4) )
& g_both(X4,X2) )
| ( ( g_true_only(X4,X4)
| g_both(X4,X4) )
& g_true_only(X4,X2) ) )
| ! [X3] :
( ~ g_both(X3,X3)
| ~ g_both(X3,X2) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
( ~ sP0
| ! [X0] :
( ? [X2] :
( ( ( g_both(X2,X2)
| g_false_only(X2,X2) )
& g_false_only(X2,X0) )
| ( ( g_true_only(X2,X2)
| g_false_only(X2,X2) )
& g_both(X2,X0) )
| ( ( g_true_only(X2,X2)
| g_both(X2,X2) )
& g_true_only(X2,X0) ) )
| ! [X1] :
( ~ g_both(X1,X1)
| ~ g_both(X1,X0) ) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ~ sP0
| ! [X0] :
( ( ( g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_false_only(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0)) )
& g_both(sK1(X0),X0) )
| ( ( g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0)) )
& g_true_only(sK1(X0),X0) )
| ! [X1] :
( ~ g_both(X1,X1)
| ~ g_both(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0))],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sP0
| g_false_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0))
| ~ g_both(X1,X1)
| ~ g_both(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sP0
| g_false_only(sK1(X0),X0)
| g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),X0)
| ~ g_both(X1,X1)
| ~ g_both(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sP0
| g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),X0)
| g_true_only(sK1(X0),X0)
| ~ g_both(X1,X1)
| ~ g_both(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( ~ sP0
| g_false_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_true_only(sK1(X0),X0)
| ~ g_both(X1,X1)
| ~ g_both(X1,X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| ~ sP0
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( g_true_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| g_false_only(sK1(X1),sK1(X1))
| g_both(sK1(X1),sK1(X1))
| ~ sP0
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_false_only(sK1(X1),sK1(X1))
| g_true_only(sK1(X1),sK1(X1))
| ~ sP0
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| g_true_only(sK1(X1),sK1(X1))
| g_both(sK1(X1),sK1(X1))
| ~ sP0
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,plain,
( g_true_only(sK1(sK2),sK2)
| g_both(sK1(sK2),sK2)
| g_false_only(sK1(sK2),sK1(sK2))
| g_both(sK1(sK2),sK1(sK2))
| ~ sP0
| ~ g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_77,c_86,c_88,c_49]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_117,plain,
( g_false_only(sK1(sK2),sK2)
| g_true_only(sK1(sK2),sK2)
| g_both(sK1(sK2),sK2)
| ~ g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| g_true_only(sK1(X1),sK1(X1))
| g_both(sK1(X1),sK1(X1))
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_77,c_86,c_88,c_53]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_both(sK1(X1),X1)
| g_true_only(sK1(X1),sK1(X1))
| g_both(sK1(X1),sK1(X1))
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(renaming,[status(thm)],[c_121]) ).
tcf(c_123,plain,
( g_false_only(sK1(sK2),sK2)
| g_both(sK1(sK2),sK2)
| g_true_only(sK1(sK2),sK1(sK2))
| g_both(sK1(sK2),sK1(sK2))
| ~ g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_false_only(sK1(X1),sK1(X1))
| g_true_only(sK1(X1),sK1(X1))
| ~ g_both(X0,X0)
| ~ g_both(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_77,c_86,c_88,c_51]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( g_false_only(sK1(X1),X1)
| g_true_only(sK1(X1),X1)
| g_false_only(sK1(X1),sK1(X1))
| g_true_only(sK1(X1),sK1(X1))
| ~ g_both(X0,X1)
| ~ g_both(X0,X0) ),
inference(renaming,[status(thm)],[c_124]) ).
tcf(c_126,plain,
( g_false_only(sK1(sK2),sK2)
| g_true_only(sK1(sK2),sK2)
| g_false_only(sK1(sK2),sK1(sK2))
| g_true_only(sK1(sK2),sK1(sK2))
| ~ g_both(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_507,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_503,c_498,c_499,c_497,c_490,c_491,c_479,c_480,c_126,c_123,c_117,c_97,c_94,c_89,c_88,c_86,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n001.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 : Thu Sep 24 15:00:53 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 2.48/1.33 % SZS status Started for theBenchmark.p
% 2.48/1.33 % SZS status Theorem for theBenchmark.p
% 2.48/1.33
% 2.48/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.48/1.33
% 2.48/1.33 % ------ iProver source info
% 2.48/1.33
% 2.48/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 2.48/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.48/1.33 % git: non_committed_changes: false
% 2.48/1.33
% 2.48/1.33 % ------ Parsing...
% 2.48/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.48/1.33
% 2.48/1.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.48/1.33
% 2.48/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.48/1.33 % ------ Proving...
% 2.48/1.33 % ------ Problem Properties
% 2.48/1.33
% 2.48/1.33 %
% 2.48/1.33 % clauses 13
% 2.48/1.33 % conjectures 6
% 2.48/1.33 % EPR 10
% 2.48/1.33 % Horn 9
% 2.48/1.33 % unary 0
% 2.48/1.33 % binary 9
% 2.48/1.33 % lits 39
% 2.48/1.33 % lits eq 0
% 2.48/1.33 % fd_pure 0
% 2.48/1.33 % fd_pseudo 0
% 2.48/1.33 % fd_cond 0
% 2.48/1.33 % fd_pseudo_cond 0
% 2.48/1.33 % AC symbols 0
% 2.48/1.33
% 2.48/1.33 % ------ Schedule dynamic 5 is on
% 2.48/1.33
% 2.48/1.33 % ------ no equalities: superposition off
% 2.48/1.33
% 2.48/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.48/1.33
% 2.48/1.33
% 2.48/1.33 % ------
% 2.48/1.33 % Current options:
% 2.48/1.33 % ------
% 2.48/1.33
% 2.48/1.33
% 2.48/1.33 %
% 2.48/1.33
% 2.48/1.33 % ------ Proving...
% 2.48/1.33 %
% 2.48/1.33
% 2.48/1.33 % SZS status Theorem for theBenchmark.p
% 2.48/1.33
% 2.48/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.48/1.33
% 2.48/1.33
%------------------------------------------------------------------------------