%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 : Tue Sep 29 10:58:52 AM UTC 2026
% Result : Unsatisfiable 1.61s 0.75s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 48
% Syntax : Number of formulae : 199 ( 199 unt; 17 def)
% Number of atoms : 199 ( 193 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 40 ( 40 usr; 35 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : or(X0,n0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).
fof(f11,axiom,
! [X0,X1] : and(X0,X1) = and(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
fof(f12,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
fof(f13,axiom,
! [X2,X0,X1] : and(X0,and(X1,X2)) = and(and(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associativity) ).
fof(f17,axiom,
! [X0,X1] : not(and(X0,X1)) = or(not(X0),not(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization1) ).
fof(f18,axiom,
! [X0,X1] : not(or(X0,X1)) = and(not(X0),not(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization2) ).
fof(f19,axiom,
! [X2,X0,X1] : and(or(X0,X1),X2) = or(and(X0,X2),and(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_canonicalization) ).
fof(f21,axiom,
! [X0,X1] : and(and(X0,X1),X1) = and(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification2) ).
fof(f22,plain,
! [X0,X1] : and(X0,X1) = and(and(X0,X1),X1),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X0,X1] : and(and(X0,X1),X0) = and(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification3) ).
fof(f24,plain,
! [X0,X1] : and(X0,X1) = and(and(X0,X1),X0),
inference(reorient_equations,[],[f23]) ).
fof(f26,axiom,
! [X0,X1] : or(or(X0,X1),X1) = or(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification2) ).
fof(f27,plain,
! [X0,X1] : or(X0,X1) = or(or(X0,X1),X1),
inference(reorient_equations,[],[f26]) ).
fof(f30,axiom,
! [X0] : and(X0,not(X0)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification1) ).
fof(f31,plain,
! [X0] : n0 = and(X0,not(X0)),
inference(reorient_equations,[],[f30]) ).
fof(f42,axiom,
! [X0] : not(not(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_simplification) ).
fof(f43,axiom,
! [X0,X1] : or(and(X0,X1),and(X0,not(X1))) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification1) ).
fof(f44,axiom,
! [X0,X1] : or(and(X0,X1),and(X1,not(X0))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification2) ).
fof(f45,negated_conjecture,
a1 = and(b1,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor1) ).
fof(f46,negated_conjecture,
a2 = and(b2,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor2) ).
fof(f47,negated_conjecture,
b1 = not(d1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor3) ).
fof(f48,negated_conjecture,
b2 = not(d2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor4) ).
fof(f49,negated_conjecture,
b3 = or(c1,c2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor5) ).
fof(f50,negated_conjecture,
c1 = or(d1,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor6) ).
fof(f51,negated_conjecture,
c2 = or(d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor7) ).
fof(f52,negated_conjecture,
d3 = f3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor8) ).
fof(f53,negated_conjecture,
d1 = not(e1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor9) ).
fof(f54,negated_conjecture,
d2 = not(e2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor10) ).
fof(f55,negated_conjecture,
e1 = or(f1,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor11) ).
fof(f56,negated_conjecture,
e2 = or(f2,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor12) ).
fof(f57,negated_conjecture,
f1 = not(i1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor13) ).
fof(f58,negated_conjecture,
f2 = not(i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor14) ).
fof(f59,negated_conjecture,
f3 = and(i1,i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor15) ).
fof(f60,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit_description) ).
fof(f61,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_interchange) ).
fof(f62,plain,
c1 = or(d1,f3),
inference(definition_unfolding,[],[f50,f52]) ).
fof(f63,plain,
c2 = or(d2,f3),
inference(definition_unfolding,[],[f51,f52]) ).
fof(f64,definition,
sF0 = and(b1,b3),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f65,plain,
and(b1,b3) = sF0,
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
a1 = sF0,
inference(definition_folding,[],[f45,f65]) ).
fof(f67,definition,
sF1 = and(b2,b3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f68,plain,
and(b2,b3) = sF1,
inference(reorient_equations,[],[f67]) ).
fof(f69,plain,
a2 = sF1,
inference(definition_folding,[],[f46,f68]) ).
fof(f70,definition,
sF2 = not(d1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f71,plain,
not(d1) = sF2,
inference(reorient_equations,[],[f70]) ).
fof(f72,plain,
b1 = sF2,
inference(definition_folding,[],[f47,f71]) ).
fof(f73,definition,
sF3 = not(d2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f74,plain,
not(d2) = sF3,
inference(reorient_equations,[],[f73]) ).
fof(f75,plain,
b2 = sF3,
inference(definition_folding,[],[f48,f74]) ).
fof(f76,definition,
sF4 = or(c1,c2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f77,plain,
or(c1,c2) = sF4,
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
b3 = sF4,
inference(definition_folding,[],[f49,f77]) ).
fof(f79,definition,
sF5 = or(d1,f3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f80,plain,
or(d1,f3) = sF5,
inference(reorient_equations,[],[f79]) ).
fof(f81,plain,
c1 = sF5,
inference(definition_folding,[],[f62,f80]) ).
fof(f82,definition,
sF6 = or(d2,f3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f83,plain,
or(d2,f3) = sF6,
inference(reorient_equations,[],[f82]) ).
fof(f84,plain,
c2 = sF6,
inference(definition_folding,[],[f63,f83]) ).
fof(f85,definition,
sF7 = not(e1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f86,plain,
not(e1) = sF7,
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
d1 = sF7,
inference(definition_folding,[],[f53,f86]) ).
fof(f88,definition,
sF8 = not(e2),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f89,plain,
not(e2) = sF8,
inference(reorient_equations,[],[f88]) ).
fof(f90,plain,
d2 = sF8,
inference(definition_folding,[],[f54,f89]) ).
fof(f91,definition,
sF9 = or(f1,f3),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f92,plain,
or(f1,f3) = sF9,
inference(reorient_equations,[],[f91]) ).
fof(f93,plain,
e1 = sF9,
inference(definition_folding,[],[f55,f92]) ).
fof(f94,definition,
sF10 = or(f2,f3),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f95,plain,
or(f2,f3) = sF10,
inference(reorient_equations,[],[f94]) ).
fof(f96,plain,
e2 = sF10,
inference(definition_folding,[],[f56,f95]) ).
fof(f97,definition,
sF11 = not(i1),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f98,plain,
not(i1) = sF11,
inference(reorient_equations,[],[f97]) ).
fof(f99,plain,
f1 = sF11,
inference(definition_folding,[],[f57,f98]) ).
fof(f100,definition,
sF12 = not(i2),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f101,plain,
not(i2) = sF12,
inference(reorient_equations,[],[f100]) ).
fof(f102,plain,
f2 = sF12,
inference(definition_folding,[],[f58,f101]) ).
fof(f103,definition,
sF13 = and(i1,i2),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f104,plain,
and(i1,i2) = sF13,
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
f3 = sF13,
inference(definition_folding,[],[f59,f104]) ).
fof(f106,definition,
sF14 = input(i1,i2),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f107,plain,
input(i1,i2) = sF14,
inference(reorient_equations,[],[f106]) ).
fof(f108,definition,
sF15 = output(a1,a2),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f109,plain,
output(a1,a2) = sF15,
inference(reorient_equations,[],[f108]) ).
fof(f110,plain,
circuit(sF14,sF15),
inference(definition_folding,[],[f60,f109,f107]) ).
fof(f111,definition,
sF16 = output(i2,i1),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f112,plain,
output(i2,i1) = sF16,
inference(reorient_equations,[],[f111]) ).
fof(f113,plain,
~ circuit(sF14,sF16),
inference(definition_folding,[],[f61,f112,f107]) ).
fof(f114,plain,
a1 = and(b1,b3),
inference(forward_demodulation,[],[f65,f66]) ).
fof(f115,plain,
a2 = and(b2,b3),
inference(forward_demodulation,[],[f68,f69]) ).
fof(f116,plain,
b1 = not(d1),
inference(forward_demodulation,[],[f71,f72]) ).
fof(f117,plain,
b2 = not(d2),
inference(forward_demodulation,[],[f74,f75]) ).
fof(f118,plain,
b3 = or(c1,c2),
inference(forward_demodulation,[],[f77,f78]) ).
fof(f119,plain,
c1 = or(d1,f3),
inference(forward_demodulation,[],[f80,f81]) ).
fof(f120,plain,
c2 = or(d2,f3),
inference(forward_demodulation,[],[f83,f84]) ).
fof(f121,plain,
d1 = not(e1),
inference(forward_demodulation,[],[f86,f87]) ).
fof(f122,plain,
d2 = not(e2),
inference(forward_demodulation,[],[f89,f90]) ).
fof(f123,plain,
e1 = or(f1,f3),
inference(forward_demodulation,[],[f92,f93]) ).
fof(f124,plain,
e2 = or(f2,f3),
inference(forward_demodulation,[],[f95,f96]) ).
fof(f125,plain,
f1 = not(i1),
inference(forward_demodulation,[],[f98,f99]) ).
fof(f126,plain,
f2 = not(i2),
inference(forward_demodulation,[],[f101,f102]) ).
fof(f127,plain,
f3 = and(i1,i2),
inference(forward_demodulation,[],[f104,f105]) ).
fof(f128,plain,
a2 = and(b3,b2),
inference(forward_demodulation,[],[f115,f11]) ).
fof(f129,plain,
e1 = or(f3,f1),
inference(forward_demodulation,[],[f123,f12]) ).
fof(f130,plain,
e2 = or(f3,f2),
inference(forward_demodulation,[],[f124,f12]) ).
fof(f133,plain,
d1 = not(b1),
inference(superposition,[],[f42,f116]) ).
fof(f137,plain,
i1 = not(f1),
inference(superposition,[],[f42,f125]) ).
fof(f138,plain,
i2 = not(f2),
inference(superposition,[],[f42,f126]) ).
fof(f153,plain,
n0 = and(i2,f2),
inference(superposition,[],[f31,f126]) ).
fof(f154,plain,
n0 = and(f2,i2),
inference(forward_demodulation,[],[f153,f11]) ).
fof(f209,plain,
! [X0] : or(n0,X0) = X0,
inference(superposition,[],[f4,f12]) ).
fof(f460,plain,
f3 = and(f3,i2),
inference(superposition,[],[f22,f127]) ).
fof(f490,plain,
f3 = and(f3,i1),
inference(superposition,[],[f24,f127]) ).
fof(f520,plain,
b3 = or(b3,c2),
inference(superposition,[],[f27,f118]) ).
fof(f585,plain,
! [X0,X1] : not(and(not(X0),X1)) = or(X0,not(X1)),
inference(superposition,[],[f17,f42]) ).
fof(f598,plain,
! [X0,X1] : not(and(X1,not(X0))) = or(not(X1),X0),
inference(superposition,[],[f17,f42]) ).
fof(f599,plain,
! [X0] : not(and(X0,b1)) = or(not(X0),d1),
inference(superposition,[],[f17,f133]) ).
fof(f636,plain,
! [X0] : or(d1,not(X0)) = not(and(X0,b1)),
inference(forward_demodulation,[],[f599,f12]) ).
fof(f654,plain,
! [X0] : not(and(X0,b1)) = not(and(not(d1),X0)),
inference(forward_demodulation,[],[f636,f585]) ).
fof(f663,plain,
! [X0] : not(and(b1,X0)) = not(and(X0,b1)),
inference(forward_demodulation,[],[f654,f116]) ).
fof(f680,plain,
not(c1) = and(not(d1),not(f3)),
inference(superposition,[],[f18,f119]) ).
fof(f681,plain,
not(c2) = and(not(d2),not(f3)),
inference(superposition,[],[f18,f120]) ).
fof(f682,plain,
not(b3) = and(not(c1),not(c2)),
inference(superposition,[],[f18,f118]) ).
fof(f683,plain,
not(e1) = and(not(f3),not(f1)),
inference(superposition,[],[f18,f129]) ).
fof(f684,plain,
not(e2) = and(not(f3),not(f2)),
inference(superposition,[],[f18,f130]) ).
fof(f695,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(superposition,[],[f42,f18]) ).
fof(f706,plain,
not(e2) = and(not(f3),i2),
inference(forward_demodulation,[],[f684,f138]) ).
fof(f707,plain,
not(e1) = and(not(f3),i1),
inference(forward_demodulation,[],[f683,f137]) ).
fof(f708,plain,
not(c2) = and(b2,not(f3)),
inference(forward_demodulation,[],[f681,f117]) ).
fof(f709,plain,
not(c1) = and(b1,not(f3)),
inference(forward_demodulation,[],[f680,f116]) ).
fof(f729,plain,
not(e2) = and(i2,not(f3)),
inference(forward_demodulation,[],[f706,f11]) ).
fof(f730,plain,
not(e1) = and(i1,not(f3)),
inference(forward_demodulation,[],[f707,f11]) ).
fof(f746,plain,
d2 = and(i2,not(f3)),
inference(forward_demodulation,[],[f729,f122]) ).
fof(f747,plain,
d1 = and(i1,not(f3)),
inference(forward_demodulation,[],[f730,f121]) ).
fof(f1066,plain,
! [X0] : and(b3,and(b2,X0)) = and(a2,X0),
inference(superposition,[],[f13,f128]) ).
fof(f2080,plain,
i2 = or(f3,and(i2,not(f3))),
inference(superposition,[],[f44,f460]) ).
fof(f2081,plain,
i2 = not(and(not(f3),not(and(i2,not(f3))))),
inference(forward_demodulation,[],[f2080,f695]) ).
fof(f2084,plain,
i2 = not(and(not(f3),not(d2))),
inference(forward_demodulation,[],[f2081,f746]) ).
fof(f2085,plain,
i2 = not(and(not(d2),not(f3))),
inference(forward_demodulation,[],[f2084,f11]) ).
fof(f2086,plain,
i2 = not(and(b2,not(f3))),
inference(forward_demodulation,[],[f2085,f117]) ).
fof(f2087,plain,
i2 = not(not(c2)),
inference(forward_demodulation,[],[f2086,f708]) ).
fof(f2088,plain,
c2 = i2,
inference(forward_demodulation,[],[f2087,f42]) ).
fof(f2367,plain,
f2 = not(c2),
inference(superposition,[],[f126,f2088]) ).
fof(f2407,plain,
! [X0] : and(or(f2,X0),i2) = or(n0,and(X0,i2)),
inference(superposition,[],[f19,f154]) ).
fof(f2492,plain,
! [X0] : and(X0,i2) = and(or(f2,X0),i2),
inference(forward_demodulation,[],[f2407,f209]) ).
fof(f2555,plain,
! [X0] : and(X0,i2) = and(i2,or(f2,X0)),
inference(forward_demodulation,[],[f2492,f11]) ).
fof(f2609,plain,
! [X0] : and(X0,i2) = and(i2,not(and(not(f2),not(X0)))),
inference(forward_demodulation,[],[f2555,f695]) ).
fof(f2657,plain,
! [X0] : and(X0,i2) = and(i2,not(and(i2,not(X0)))),
inference(forward_demodulation,[],[f2609,f138]) ).
fof(f2674,plain,
! [X0] : and(X0,c2) = and(c2,not(and(c2,not(X0)))),
inference(forward_demodulation,[],[f2657,f2088]) ).
fof(f2690,plain,
c2 = not(f2),
inference(superposition,[],[f42,f2367]) ).
fof(f2908,plain,
not(b3) = and(not(b3),not(c2)),
inference(superposition,[],[f18,f520]) ).
fof(f2913,plain,
not(b3) = and(not(b3),f2),
inference(forward_demodulation,[],[f2908,f2367]) ).
fof(f2917,plain,
not(b3) = and(f2,not(b3)),
inference(forward_demodulation,[],[f2913,f11]) ).
fof(f3613,plain,
d2 = and(c2,not(f3)),
inference(superposition,[],[f746,f2088]) ).
fof(f3706,plain,
i1 = or(and(f3,i1),d1),
inference(superposition,[],[f44,f747]) ).
fof(f3728,plain,
i1 = or(d1,and(f3,i1)),
inference(forward_demodulation,[],[f3706,f12]) ).
fof(f3734,plain,
i1 = not(and(not(d1),not(and(f3,i1)))),
inference(forward_demodulation,[],[f3728,f695]) ).
fof(f3740,plain,
i1 = not(and(not(d1),not(f3))),
inference(forward_demodulation,[],[f3734,f490]) ).
fof(f3746,plain,
i1 = not(and(b1,not(f3))),
inference(forward_demodulation,[],[f3740,f116]) ).
fof(f3752,plain,
i1 = not(not(c1)),
inference(forward_demodulation,[],[f3746,f709]) ).
fof(f3757,plain,
c1 = i1,
inference(forward_demodulation,[],[f3752,f42]) ).
fof(f3765,plain,
sF16 = output(i2,c1),
inference(superposition,[],[f112,f3757]) ).
fof(f3766,plain,
f1 = not(c1),
inference(superposition,[],[f125,f3757]) ).
fof(f3767,plain,
f3 = and(c1,i2),
inference(superposition,[],[f127,f3757]) ).
fof(f3777,plain,
f3 = and(c1,c2),
inference(forward_demodulation,[],[f3767,f2088]) ).
fof(f3778,plain,
sF16 = output(c2,c1),
inference(forward_demodulation,[],[f3765,f2088]) ).
fof(f3856,plain,
c1 = not(f1),
inference(superposition,[],[f42,f3766]) ).
fof(f4841,plain,
not(c1) = or(not(b3),and(not(c1),not(not(c2)))),
inference(superposition,[],[f43,f682]) ).
fof(f4844,plain,
not(c1) = not(and(b3,not(and(not(c1),not(not(c2)))))),
inference(forward_demodulation,[],[f4841,f598]) ).
fof(f4858,plain,
not(c1) = not(and(b3,not(and(not(c1),c2)))),
inference(forward_demodulation,[],[f4844,f42]) ).
fof(f4871,plain,
not(c1) = not(and(b3,not(and(c2,not(and(c2,not(not(c1)))))))),
inference(forward_demodulation,[],[f4858,f2674]) ).
fof(f4882,plain,
not(c1) = not(and(b3,not(and(c2,not(and(c2,c1)))))),
inference(forward_demodulation,[],[f4871,f42]) ).
fof(f4890,plain,
not(c1) = not(and(b3,not(and(c2,not(and(c1,c2)))))),
inference(forward_demodulation,[],[f4882,f11]) ).
fof(f4896,plain,
not(c1) = not(and(b3,not(and(c2,not(f3))))),
inference(forward_demodulation,[],[f4890,f3777]) ).
fof(f4899,plain,
not(c1) = not(and(b3,not(d2))),
inference(forward_demodulation,[],[f4896,f3613]) ).
fof(f4902,plain,
not(c1) = not(and(b3,b2)),
inference(forward_demodulation,[],[f4899,f117]) ).
fof(f4904,plain,
not(c1) = not(a2),
inference(forward_demodulation,[],[f4902,f128]) ).
fof(f4906,plain,
f1 = not(a2),
inference(forward_demodulation,[],[f4904,f3766]) ).
fof(f4916,plain,
a2 = not(f1),
inference(superposition,[],[f42,f4906]) ).
fof(f5087,plain,
a2 = c1,
inference(superposition,[],[f3856,f4916]) ).
fof(f5088,plain,
a2 = i1,
inference(superposition,[],[f137,f4916]) ).
fof(f5305,plain,
d1 = and(a2,not(f3)),
inference(superposition,[],[f747,f5088]) ).
fof(f6598,plain,
and(a2,not(f3)) = and(b3,not(c2)),
inference(superposition,[],[f1066,f708]) ).
fof(f6637,plain,
and(b3,f2) = and(a2,not(f3)),
inference(forward_demodulation,[],[f6598,f2367]) ).
fof(f6647,plain,
d1 = and(b3,f2),
inference(forward_demodulation,[],[f6637,f5305]) ).
fof(f6662,plain,
f2 = or(d1,and(f2,not(b3))),
inference(superposition,[],[f44,f6647]) ).
fof(f6663,plain,
f2 = not(and(not(d1),not(and(f2,not(b3))))),
inference(forward_demodulation,[],[f6662,f695]) ).
fof(f6673,plain,
f2 = not(and(not(d1),not(not(b3)))),
inference(forward_demodulation,[],[f6663,f2917]) ).
fof(f6679,plain,
f2 = not(and(not(d1),b3)),
inference(forward_demodulation,[],[f6673,f42]) ).
fof(f6683,plain,
f2 = not(and(b3,not(d1))),
inference(forward_demodulation,[],[f6679,f11]) ).
fof(f6687,plain,
f2 = not(and(b3,b1)),
inference(forward_demodulation,[],[f6683,f116]) ).
fof(f6690,plain,
f2 = not(and(b1,b3)),
inference(forward_demodulation,[],[f6687,f663]) ).
fof(f6693,plain,
f2 = not(a1),
inference(forward_demodulation,[],[f6690,f114]) ).
fof(f6817,plain,
a1 = not(f2),
inference(superposition,[],[f42,f6693]) ).
fof(f7001,plain,
a1 = c2,
inference(superposition,[],[f2690,f6817]) ).
fof(f7152,plain,
sF16 = output(a1,c1),
inference(superposition,[],[f3778,f7001]) ).
fof(f7153,plain,
output(a1,a2) = sF16,
inference(forward_demodulation,[],[f7152,f5087]) ).
fof(f7167,plain,
sF15 = sF16,
inference(forward_demodulation,[],[f7153,f109]) ).
fof(f7483,plain,
~ circuit(sF14,sF15),
inference(superposition,[],[f113,f7167]) ).
fof(f7484,plain,
$false,
inference(forward_subsumption_resolution,[],[f7483,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n003.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:53:41 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.61/0.75 % (338575)Will run a generic schedule for satisfiability detection.
% 1.61/0.75 % (338586)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=247999611:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.61/0.75 % (338581)% WARNING: option uhcvi not known.
% 1.61/0.75 % (338584)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3970712303:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.61/0.75 % (338580)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3674750335_2999 on theBenchmark for (2999ds/0Mi)
% 1.61/0.75 % (338581)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3846107317:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.61/0.75 % (338582)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=544540236:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.61/0.75 % (338583)dis+10_1_sil=32000:sp=arity:random_seed=1932113781:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.61/0.75 % (338585)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2577619708:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.61/0.75 % TRYING [1]
% 1.61/0.75 % TRYING [2]
% 1.61/0.75 % TRYING [3]
% 1.61/0.75 % TRYING [4]
% 1.61/0.75 % (338586)Instruction limit reached!
% 1.61/0.75 % (338586)------------------------------
% 1.61/0.75 % (338586)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % TRYING [5]
% 1.61/0.75 % (338586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338586)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338586)Termination reason: Instruction limit
% 1.61/0.75 % (338586)Termination phase: Saturation
% 1.61/0.75 % (338586)Time elapsed: 0.047 s
% 1.61/0.75 % (338586)Peak memory usage: 13 MB
% 1.61/0.75 % (338586)Instructions burned: 159 (million)
% 1.61/0.75 % (338594)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=73250105:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.61/0.75 % TRYING [1]
% 1.61/0.75 % TRYING [2]
% 1.61/0.75 % TRYING [3]
% 1.61/0.75 % (338583)Instruction limit reached!
% 1.61/0.75 % (338583)------------------------------
% 1.61/0.75 % (338583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338583)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338583)Termination reason: Instruction limit
% 1.61/0.75 % (338583)Termination phase: Saturation
% 1.61/0.75 % (338583)Time elapsed: 0.056 s
% 1.61/0.75 % (338583)Peak memory usage: 12 MB
% 1.61/0.75 % (338583)Instructions burned: 104 (million)
% 1.61/0.75 % TRYING [4]
% 1.61/0.75 % (338584)Instruction limit reached!
% 1.61/0.75 % (338584)------------------------------
% 1.61/0.75 % (338584)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338584)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338584)Termination reason: Instruction limit
% 1.61/0.75 % (338584)Termination phase: Saturation
% 1.61/0.75 % (338584)Time elapsed: 0.068 s
% 1.61/0.75 % (338584)Peak memory usage: 13 MB
% 1.61/0.75 % (338584)Instructions burned: 122 (million)
% 1.61/0.75 % TRYING [5]
% 1.61/0.75 % (338585)Instruction limit reached!
% 1.61/0.75 % (338585)------------------------------
% 1.61/0.75 % (338585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338585)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338585)Termination reason: Instruction limit
% 1.61/0.75 % (338585)Termination phase: Saturation
% 1.61/0.75 % (338585)Time elapsed: 0.075 s
% 1.61/0.75 % (338585)Peak memory usage: 13 MB
% 1.61/0.75 % (338585)Instructions burned: 132 (million)
% 1.61/0.75 % (338596)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=84198374:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.61/0.75 % (338597)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1173575268:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.61/0.75 % (338598)ott-21_1_sil=16000:fs=off:random_seed=2901092362:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.61/0.75 % TRYING [6]
% 1.61/0.75 % TRYING [6]
% 1.61/0.75 % (338596)Instruction limit reached!
% 1.61/0.75 % (338596)------------------------------
% 1.61/0.75 % (338596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338596)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338596)Termination reason: Instruction limit
% 1.61/0.75 % (338596)Termination phase: Saturation
% 1.61/0.75 % (338596)Time elapsed: 0.085 s
% 1.61/0.75 % (338596)Peak memory usage: 13 MB
% 1.61/0.75 % (338596)Instructions burned: 131 (million)
% 1.61/0.75 % (338598)Instruction limit reached!
% 1.61/0.75 % (338598)------------------------------
% 1.61/0.75 % (338598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338598)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338598)Termination reason: Instruction limit
% 1.61/0.75 % (338598)Termination phase: Saturation
% 1.61/0.75 % (338598)Time elapsed: 0.085 s
% 1.61/0.75 % (338598)Peak memory usage: 13 MB
% 1.61/0.75 % (338598)Instructions burned: 180 (million)
% 1.61/0.75 % (338602)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3989432678:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.61/0.75 % (338603)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3696870935:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.61/0.75 % (338594)Instruction limit reached!
% 1.61/0.75 % (338594)------------------------------
% 1.61/0.75 % (338594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338594)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338594)Termination reason: Instruction limit
% 1.61/0.75 % (338594)Termination phase: Finite model building SAT solving
% 1.61/0.75 % (338594)Time elapsed: 0.152 s
% 1.61/0.75 % (338594)Peak memory usage: 32 MB
% 1.61/0.75 % (338594)Instructions burned: 714 (million)
% 1.61/0.75 % TRYING [1]
% 1.61/0.75 % TRYING [2]
% 1.61/0.75 % TRYING [3]
% 1.61/0.75 % (338606)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2914878978:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.61/0.75 % TRYING [4]
% 1.61/0.75 % TRYING [7]
% 1.61/0.75 % TRYING [5]
% 1.61/0.75 % (338606) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-338575-338606"...
% 1.61/0.75 % (338606)...printing done.
% 1.61/0.75 % (338606)Refutation found. Thanks to Tanya!
% 1.61/0.75 % SZS status Unsatisfiable for theBenchmark
% 1.61/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 1.61/0.75 % (338606)------------------------------
% 1.61/0.75 % (338606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.61/0.75 % (338606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/0.75 % (338606)CaDiCaL version: 2.1.3
% 1.61/0.75 % (338606)Termination reason: Refutation
% 1.61/0.75 % (338606)Time elapsed: 0.063 s
% 1.61/0.75 % (338606)Peak memory usage: 14 MB
% 1.61/0.75 % (338606)Instructions burned: 217 (million)
% 1.61/0.75 % (338575)Success in time 0.317 s
% 1.61/0.75 % Vampire exiting
%------------------------------------------------------------------------------