%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL315-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:51:57 AM UTC 2026
% Result : Unsatisfiable 11.51s 8.07s
% Output : Refutation 11.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 33
% Syntax : Number of formulae : 192 ( 192 unt; 21 def)
% Number of atoms : 192 ( 191 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 25 con; 0-4 aty)
% Number of variables : 173 ( 173 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f4,plain,
! [X0,X1] : true = axiom(implies(X0,or(X1,X0))),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f6,plain,
! [X0,X1] : true = axiom(implies(or(X0,X1),or(X1,X0))),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f8,plain,
! [X2,X0,X1] : true = axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f10,plain,
! [X2,X0,X1] : true = axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f12,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f13,plain,
! [X0] : true = ifeq(axiom(X0),true,theorem(X0),true),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] : ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f15,plain,
! [X0,X1] : true = ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f17,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f18,negated_conjecture,
theorem(implies(equivalent(p,q),equivalent(implies(p,r),implies(q,r)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f19,plain,
true != theorem(implies(equivalent(p,q),equivalent(implies(p,r),implies(q,r)))),
inference(reorient_equations,[],[f18]) ).
fof(f20,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f17,f16,f11,f11]) ).
fof(f21,plain,
true != theorem(or(not(not(or(not(or(not(p),q)),not(or(not(q),p))))),not(or(not(or(not(or(not(p),r)),or(not(q),r))),not(or(not(or(not(q),r)),or(not(p),r))))))),
inference(definition_unfolding,[],[f19,f11,f20,f20,f11,f11]) ).
fof(f22,plain,
! [X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true),
inference(definition_unfolding,[],[f15,f11]) ).
fof(f23,plain,
! [X2,X0,X1] : true = axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f10,f11,f11,f11]) ).
fof(f24,plain,
! [X2,X0,X1] : true = axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f8,f11]) ).
fof(f25,plain,
! [X0,X1] : true = axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f6,f11]) ).
fof(f26,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f4,f11]) ).
fof(f27,plain,
! [X0] : true = axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f2,f11]) ).
fof(f28,definition,
sF0 = not(p),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f29,plain,
not(p) = sF0,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF1 = or(sF0,q),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f31,plain,
or(sF0,q) = sF1,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF2 = not(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f33,plain,
not(sF1) = sF2,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF3 = not(q),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f35,plain,
not(q) = sF3,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF4 = or(sF3,p),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f37,plain,
or(sF3,p) = sF4,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF5 = not(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f39,plain,
not(sF4) = sF5,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF6 = or(sF2,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f41,plain,
or(sF2,sF5) = sF6,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF7 = not(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f43,plain,
not(sF6) = sF7,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF8 = not(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f45,plain,
not(sF7) = sF8,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF9 = or(sF0,r),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f47,plain,
or(sF0,r) = sF9,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF10 = not(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f49,plain,
not(sF9) = sF10,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF11 = or(sF3,r),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f51,plain,
or(sF3,r) = sF11,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF12 = or(sF10,sF11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f53,plain,
or(sF10,sF11) = sF12,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF13 = not(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f55,plain,
not(sF12) = sF13,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF14 = not(sF11),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f57,plain,
not(sF11) = sF14,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF15 = or(sF14,sF9),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f59,plain,
or(sF14,sF9) = sF15,
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
sF16 = not(sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f61,plain,
not(sF15) = sF16,
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
sF17 = or(sF13,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f63,plain,
or(sF13,sF16) = sF17,
inference(reorient_equations,[],[f62]) ).
fof(f64,definition,
sF18 = not(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f65,plain,
not(sF17) = sF18,
inference(reorient_equations,[],[f64]) ).
fof(f66,definition,
sF19 = or(sF8,sF18),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f67,plain,
or(sF8,sF18) = sF19,
inference(reorient_equations,[],[f66]) ).
fof(f68,definition,
sF20 = theorem(sF19),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f69,plain,
theorem(sF19) = sF20,
inference(reorient_equations,[],[f68]) ).
fof(f70,plain,
true != sF20,
inference(definition_folding,[],[f21,f69,f67,f65,f63,f61,f59,f47,f29,f57,f51,f35,f55,f53,f51,f35,f49,f47,f29,f45,f43,f41,f39,f37,f35,f33,f31,f29]) ).
fof(f94,plain,
! [X0] : true = ifeq(theorem(or(not(X0),sF19)),true,ifeq(theorem(X0),true,sF20,true),true),
inference(superposition,[],[f22,f69]) ).
fof(f96,plain,
! [X0] : true = axiom(or(not(or(not(p),X0)),or(not(sF4),or(sF3,X0)))),
inference(superposition,[],[f23,f37]) ).
fof(f102,plain,
! [X0] : true = axiom(or(not(or(not(p),X0)),or(sF5,or(sF3,X0)))),
inference(forward_demodulation,[],[f96,f39]) ).
fof(f103,plain,
! [X0] : true = axiom(or(not(or(sF0,X0)),or(sF5,or(sF3,X0)))),
inference(forward_demodulation,[],[f102,f29]) ).
fof(f105,plain,
! [X0] : true = axiom(or(not(or(not(q),X0)),or(not(sF1),or(sF0,X0)))),
inference(superposition,[],[f23,f31]) ).
fof(f111,plain,
! [X0] : true = axiom(or(not(or(not(q),X0)),or(sF2,or(sF0,X0)))),
inference(forward_demodulation,[],[f105,f33]) ).
fof(f112,plain,
! [X0] : true = axiom(or(not(or(sF3,X0)),or(sF2,or(sF0,X0)))),
inference(forward_demodulation,[],[f111,f35]) ).
fof(f169,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true),
inference(superposition,[],[f13,f25]) ).
fof(f170,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),true),
inference(superposition,[],[f13,f24]) ).
fof(f171,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),true),
inference(superposition,[],[f13,f23]) ).
fof(f172,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,X0)),X0)),true),
inference(superposition,[],[f13,f27]) ).
fof(f174,plain,
! [X0] : true = theorem(or(not(or(X0,X0)),X0)),
inference(forward_demodulation,[],[f172,f1]) ).
fof(f175,plain,
! [X2,X0,X1] : true = theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(forward_demodulation,[],[f171,f1]) ).
fof(f176,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(forward_demodulation,[],[f170,f1]) ).
fof(f177,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(forward_demodulation,[],[f169,f1]) ).
fof(f196,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),true),
inference(superposition,[],[f22,f176]) ).
fof(f202,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X1,or(X0,X2))),true),
inference(forward_demodulation,[],[f196,f1]) ).
fof(f232,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(not(X0),X1)),true,theorem(or(not(or(X2,X0)),or(X2,X1))),true),true),
inference(superposition,[],[f22,f175]) ).
fof(f238,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,theorem(or(not(or(X2,X0)),or(X2,X1))),true),
inference(forward_demodulation,[],[f232,f1]) ).
fof(f271,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X1,X0))),true),
inference(superposition,[],[f13,f26]) ).
fof(f272,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X1,X0))),
inference(forward_demodulation,[],[f271,f1]) ).
fof(f302,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),true),
inference(superposition,[],[f22,f177]) ).
fof(f308,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),
inference(forward_demodulation,[],[f302,f1]) ).
fof(f448,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f238,f177]) ).
fof(f449,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),true),
inference(superposition,[],[f238,f174]) ).
fof(f450,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,X0)),or(X2,or(X1,X0)))),true),
inference(superposition,[],[f238,f272]) ).
fof(f484,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,X0)),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f450,f1]) ).
fof(f485,plain,
! [X0,X1] : true = theorem(or(not(or(X1,or(X0,X0))),or(X1,X0))),
inference(forward_demodulation,[],[f449,f1]) ).
fof(f486,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,or(X0,X1))),or(X2,or(X1,X0)))),
inference(forward_demodulation,[],[f448,f1]) ).
fof(f514,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),true),
inference(superposition,[],[f22,f486]) ).
fof(f522,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,or(X1,X2))),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f514,f1]) ).
fof(f540,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X0),or(X0,X1))),true),
inference(superposition,[],[f522,f272]) ).
fof(f559,plain,
! [X0,X1] : true = theorem(or(not(X0),or(X0,X1))),
inference(forward_demodulation,[],[f540,f1]) ).
fof(f602,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X2,X1))),true),true),
inference(superposition,[],[f22,f484]) ).
fof(f613,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X2,X1))),true),
inference(forward_demodulation,[],[f602,f1]) ).
fof(f698,plain,
! [X2,X0,X1] : true = ifeq(true,true,theorem(or(not(or(X2,X0)),or(X2,or(X0,X1)))),true),
inference(superposition,[],[f238,f559]) ).
fof(f715,plain,
! [X2,X0,X1] : true = theorem(or(not(or(X2,X0)),or(X2,or(X0,X1)))),
inference(forward_demodulation,[],[f698,f1]) ).
fof(f759,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),true),
inference(superposition,[],[f22,f485]) ).
fof(f775,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,or(X1,X1))),true,theorem(or(X0,X1)),true),
inference(forward_demodulation,[],[f759,f1]) ).
fof(f785,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(X0),X0)),true),
inference(superposition,[],[f775,f559]) ).
fof(f808,plain,
! [X0] : true = theorem(or(not(X0),X0)),
inference(forward_demodulation,[],[f785,f1]) ).
fof(f838,plain,
! [X0] : true = ifeq(true,true,theorem(or(X0,not(X0))),true),
inference(superposition,[],[f308,f808]) ).
fof(f846,plain,
! [X0] : true = theorem(or(X0,not(X0))),
inference(forward_demodulation,[],[f838,f1]) ).
fof(f870,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X1,X0)),or(X1,not(not(X0))))),true),
inference(superposition,[],[f238,f846]) ).
fof(f888,plain,
! [X0,X1] : true = theorem(or(not(or(X1,X0)),or(X1,not(not(X0))))),
inference(forward_demodulation,[],[f870,f1]) ).
fof(f912,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X0,not(not(X1)))),true),true),
inference(superposition,[],[f22,f888]) ).
fof(f914,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(not(not(X1)),X0))),true),
inference(superposition,[],[f522,f888]) ).
fof(f931,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(not(not(X1)),X0))),
inference(forward_demodulation,[],[f914,f1]) ).
fof(f932,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X0,not(not(X1)))),true),
inference(forward_demodulation,[],[f912,f1]) ).
fof(f969,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(not(not(X1)),X0)),true),true),
inference(superposition,[],[f22,f931]) ).
fof(f989,plain,
! [X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(not(not(X1)),X0)),true),
inference(forward_demodulation,[],[f969,f1]) ).
fof(f1041,plain,
! [X0] : true = ifeq(theorem(or(X0,sF5)),true,theorem(or(X0,sF6)),true),
inference(superposition,[],[f613,f41]) ).
fof(f1195,plain,
true = axiom(or(not(or(sF3,r)),or(sF2,sF9))),
inference(superposition,[],[f112,f47]) ).
fof(f1198,plain,
true = axiom(or(not(sF11),or(sF2,sF9))),
inference(forward_demodulation,[],[f1195,f51]) ).
fof(f1201,plain,
true = axiom(or(sF14,or(sF2,sF9))),
inference(forward_demodulation,[],[f1198,f57]) ).
fof(f1221,plain,
true = axiom(or(not(or(sF0,r)),or(sF5,sF11))),
inference(superposition,[],[f103,f51]) ).
fof(f1224,plain,
true = axiom(or(not(sF9),or(sF5,sF11))),
inference(forward_demodulation,[],[f1221,f47]) ).
fof(f1227,plain,
true = axiom(or(sF10,or(sF5,sF11))),
inference(forward_demodulation,[],[f1224,f49]) ).
fof(f1287,plain,
true = ifeq(true,true,theorem(or(sF10,or(sF5,sF11))),true),
inference(superposition,[],[f13,f1227]) ).
fof(f1288,plain,
true = theorem(or(sF10,or(sF5,sF11))),
inference(forward_demodulation,[],[f1287,f1]) ).
fof(f1294,plain,
true = ifeq(true,true,theorem(or(sF5,or(sF10,sF11))),true),
inference(superposition,[],[f202,f1288]) ).
fof(f1311,plain,
true = theorem(or(sF5,or(sF10,sF11))),
inference(forward_demodulation,[],[f1294,f1]) ).
fof(f1314,plain,
true = theorem(or(sF5,sF12)),
inference(forward_demodulation,[],[f1311,f53]) ).
fof(f1320,plain,
true = ifeq(true,true,theorem(or(sF12,sF5)),true),
inference(superposition,[],[f308,f1314]) ).
fof(f1328,plain,
true = theorem(or(sF12,sF5)),
inference(forward_demodulation,[],[f1320,f1]) ).
fof(f1332,plain,
true = ifeq(true,true,theorem(or(sF12,sF6)),true),
inference(superposition,[],[f1041,f1328]) ).
fof(f1348,plain,
true = theorem(or(sF12,sF6)),
inference(forward_demodulation,[],[f1332,f1]) ).
fof(f1388,plain,
true = ifeq(true,true,theorem(or(sF14,or(sF2,sF9))),true),
inference(superposition,[],[f13,f1201]) ).
fof(f1389,plain,
true = theorem(or(sF14,or(sF2,sF9))),
inference(forward_demodulation,[],[f1388,f1]) ).
fof(f1395,plain,
true = ifeq(true,true,theorem(or(sF2,or(sF14,sF9))),true),
inference(superposition,[],[f202,f1389]) ).
fof(f1412,plain,
true = theorem(or(sF2,or(sF14,sF9))),
inference(forward_demodulation,[],[f1395,f1]) ).
fof(f1415,plain,
true = theorem(or(sF2,sF15)),
inference(forward_demodulation,[],[f1412,f59]) ).
fof(f1421,plain,
true = ifeq(true,true,theorem(or(sF15,sF2)),true),
inference(superposition,[],[f308,f1415]) ).
fof(f1429,plain,
true = theorem(or(sF15,sF2)),
inference(forward_demodulation,[],[f1421,f1]) ).
fof(f1620,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X1,X2))),true),true),
inference(superposition,[],[f22,f715]) ).
fof(f1646,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(X0,X1)),true,theorem(or(X0,or(X1,X2))),true),
inference(forward_demodulation,[],[f1620,f1]) ).
fof(f1695,plain,
! [X0] : true = ifeq(theorem(or(X0,sF2)),true,theorem(or(X0,sF6)),true),
inference(superposition,[],[f1646,f41]) ).
fof(f1698,plain,
! [X0] : true = ifeq(theorem(or(X0,sF8)),true,theorem(or(X0,sF19)),true),
inference(superposition,[],[f1646,f67]) ).
fof(f1784,plain,
true = ifeq(true,true,theorem(or(sF15,sF6)),true),
inference(superposition,[],[f1695,f1429]) ).
fof(f1789,plain,
true = theorem(or(sF15,sF6)),
inference(forward_demodulation,[],[f1784,f1]) ).
fof(f3715,plain,
true = ifeq(true,true,theorem(or(sF12,not(not(sF6)))),true),
inference(superposition,[],[f932,f1348]) ).
fof(f3723,plain,
true = ifeq(true,true,theorem(or(sF15,not(not(sF6)))),true),
inference(superposition,[],[f932,f1789]) ).
fof(f3752,plain,
true = theorem(or(sF15,not(not(sF6)))),
inference(forward_demodulation,[],[f3723,f1]) ).
fof(f3760,plain,
true = theorem(or(sF12,not(not(sF6)))),
inference(forward_demodulation,[],[f3715,f1]) ).
fof(f3828,plain,
true = theorem(or(sF15,not(sF7))),
inference(forward_demodulation,[],[f3752,f43]) ).
fof(f3833,plain,
true = theorem(or(sF12,not(sF7))),
inference(forward_demodulation,[],[f3760,f43]) ).
fof(f3856,plain,
true = theorem(or(sF15,sF8)),
inference(forward_demodulation,[],[f3828,f45]) ).
fof(f3857,plain,
true = theorem(or(sF12,sF8)),
inference(forward_demodulation,[],[f3833,f45]) ).
fof(f3859,plain,
true = ifeq(true,true,theorem(or(sF8,sF12)),true),
inference(superposition,[],[f308,f3857]) ).
fof(f3878,plain,
true = theorem(or(sF8,sF12)),
inference(forward_demodulation,[],[f3859,f1]) ).
fof(f3881,plain,
true = ifeq(true,true,theorem(or(sF8,sF15)),true),
inference(superposition,[],[f308,f3856]) ).
fof(f3900,plain,
true = theorem(or(sF8,sF15)),
inference(forward_demodulation,[],[f3881,f1]) ).
fof(f4667,plain,
true = ifeq(true,true,theorem(or(not(not(sF12)),sF8)),true),
inference(superposition,[],[f989,f3878]) ).
fof(f4668,plain,
true = ifeq(true,true,theorem(or(not(not(sF15)),sF8)),true),
inference(superposition,[],[f989,f3900]) ).
fof(f4752,plain,
true = theorem(or(not(not(sF15)),sF8)),
inference(forward_demodulation,[],[f4668,f1]) ).
fof(f4753,plain,
true = theorem(or(not(not(sF12)),sF8)),
inference(forward_demodulation,[],[f4667,f1]) ).
fof(f4831,plain,
true = theorem(or(not(sF16),sF8)),
inference(forward_demodulation,[],[f4752,f61]) ).
fof(f4832,plain,
true = theorem(or(not(sF13),sF8)),
inference(forward_demodulation,[],[f4753,f55]) ).
fof(f5168,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,sF16)),or(X0,sF8))),true),
inference(superposition,[],[f238,f4831]) ).
fof(f5196,plain,
! [X0] : true = theorem(or(not(or(X0,sF16)),or(X0,sF8))),
inference(forward_demodulation,[],[f5168,f1]) ).
fof(f5198,plain,
true = theorem(or(not(sF17),or(sF13,sF8))),
inference(superposition,[],[f5196,f63]) ).
fof(f5245,plain,
true = theorem(or(sF18,or(sF13,sF8))),
inference(forward_demodulation,[],[f5198,f65]) ).
fof(f5257,plain,
true = ifeq(true,true,theorem(or(sF13,or(sF18,sF8))),true),
inference(superposition,[],[f202,f5245]) ).
fof(f5287,plain,
true = theorem(or(sF13,or(sF18,sF8))),
inference(forward_demodulation,[],[f5257,f1]) ).
fof(f5290,plain,
! [X0] : true = ifeq(true,true,theorem(or(not(or(X0,sF13)),or(X0,sF8))),true),
inference(superposition,[],[f238,f4832]) ).
fof(f5319,plain,
! [X0] : true = theorem(or(not(or(X0,sF13)),or(X0,sF8))),
inference(forward_demodulation,[],[f5290,f1]) ).
fof(f5328,plain,
! [X0] : true = ifeq(true,true,ifeq(theorem(or(X0,sF13)),true,theorem(or(X0,sF8)),true),true),
inference(superposition,[],[f22,f5319]) ).
fof(f5362,plain,
! [X0] : true = ifeq(theorem(or(X0,sF13)),true,theorem(or(X0,sF8)),true),
inference(forward_demodulation,[],[f5328,f1]) ).
fof(f5509,plain,
true = ifeq(true,true,theorem(or(sF13,or(sF8,sF18))),true),
inference(superposition,[],[f522,f5287]) ).
fof(f5536,plain,
true = theorem(or(sF13,or(sF8,sF18))),
inference(forward_demodulation,[],[f5509,f1]) ).
fof(f5544,plain,
true = theorem(or(sF13,sF19)),
inference(forward_demodulation,[],[f5536,f67]) ).
fof(f5553,plain,
true = ifeq(true,true,theorem(or(sF19,sF13)),true),
inference(superposition,[],[f308,f5544]) ).
fof(f5574,plain,
true = theorem(or(sF19,sF13)),
inference(forward_demodulation,[],[f5553,f1]) ).
fof(f5690,plain,
true = ifeq(true,true,theorem(or(sF19,sF8)),true),
inference(superposition,[],[f5362,f5574]) ).
fof(f5719,plain,
true = theorem(or(sF19,sF8)),
inference(forward_demodulation,[],[f5690,f1]) ).
fof(f5775,plain,
true = ifeq(true,true,theorem(or(sF19,sF19)),true),
inference(superposition,[],[f1698,f5719]) ).
fof(f5798,plain,
true = theorem(or(sF19,sF19)),
inference(forward_demodulation,[],[f5775,f1]) ).
fof(f6074,plain,
true = ifeq(theorem(or(not(or(sF19,sF19)),sF19)),true,ifeq(true,true,sF20,true),true),
inference(superposition,[],[f94,f5798]) ).
fof(f6080,plain,
true = ifeq(theorem(or(not(or(sF19,sF19)),sF19)),true,sF20,true),
inference(forward_demodulation,[],[f6074,f1]) ).
fof(f6087,plain,
true = ifeq(true,true,sF20,true),
inference(forward_demodulation,[],[f6080,f174]) ).
fof(f6088,plain,
true = sF20,
inference(forward_demodulation,[],[f6087,f1]) ).
fof(f6089,plain,
$false,
inference(forward_subsumption_resolution,[],[f6088,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL315-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/6.18 % Computer : n012.cluster.edu
% 0.07/6.18 % Model : x86_64 x86_64
% 0.07/6.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/6.18 % Memory : 8046.5625MB
% 0.07/6.18 % OS : Linux 6.8.0-71-generic
% 0.07/6.18 % CPULimit : 300
% 0.07/6.18 % WCLimit : 300
% 0.07/6.18 % DateTime : Sun Sep 27 15:33:49 UTC 2026
% 0.07/6.18 % CPUTime :
% 0.07/6.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/6.20 Running first-order theorem proving
% 0.10/6.20 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.51/8.07 % (2523936)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.51/8.07 % (2523954)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3945906870:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.51/8.07 % (2523955)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2103437636:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.51/8.07 % (2523957)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3733591835:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.51/8.07 % (2523960)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3969142405:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.51/8.07 % (2523958)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1790780198:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.51/8.07 % (2523956)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3908275850:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.51/8.07 % (2523959)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=34123836:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.51/8.07 % (2523957)Instruction limit reached!
% 11.51/8.07 % (2523957)------------------------------
% 11.51/8.07 % (2523957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523957)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523957)Termination reason: Instruction limit
% 11.51/8.07 % (2523957)Termination phase: Saturation
% 11.51/8.07 % (2523957)Time elapsed: 0.046 s
% 11.51/8.07 % (2523957)Peak memory usage: 89 MB
% 11.51/8.07 % (2523957)Instructions burned: 138 (million)
% 11.51/8.07 % (2523958)Instruction limit reached!
% 11.51/8.07 % (2523958)------------------------------
% 11.51/8.07 % (2523958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523958)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523958)Termination reason: Instruction limit
% 11.51/8.07 % (2523958)Termination phase: Saturation
% 11.51/8.07 % (2523958)Time elapsed: 0.056 s
% 11.51/8.07 % (2523958)Peak memory usage: 89 MB
% 11.51/8.07 % (2523958)Instructions burned: 184 (million)
% 11.51/8.07 % (2523959)Instruction limit reached!
% 11.51/8.07 % (2523959)------------------------------
% 11.51/8.07 % (2523959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523959)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523959)Termination reason: Instruction limit
% 11.51/8.07 % (2523959)Termination phase: Saturation
% 11.51/8.07 % (2523959)Time elapsed: 0.082 s
% 11.51/8.07 % (2523959)Peak memory usage: 90 MB
% 11.51/8.07 % (2523959)Instructions burned: 259 (million)
% 11.51/8.07 % (2523986)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4277542912:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 11.51/8.07 % (2523985)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3613075678:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 11.51/8.07 % (2523987)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1516140834:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 11.51/8.07 % (2523987)Instruction limit reached!
% 11.51/8.07 % (2523987)------------------------------
% 11.51/8.07 % (2523987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523987)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523987)Termination reason: Instruction limit
% 11.51/8.07 % (2523987)Termination phase: Saturation
% 11.51/8.07 % (2523987)Time elapsed: 0.059 s
% 11.51/8.07 % (2523987)Peak memory usage: 88 MB
% 11.51/8.07 % (2523987)Instructions burned: 218 (million)
% 11.51/8.07 % (2523960)Instruction limit reached!
% 11.51/8.07 % (2523960)------------------------------
% 11.51/8.07 % (2523960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523960)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523960)Termination reason: Instruction limit
% 11.51/8.07 % (2523960)Termination phase: Saturation
% 11.51/8.07 % (2523960)Time elapsed: 0.379 s
% 11.51/8.07 % (2523960)Peak memory usage: 101 MB
% 11.51/8.07 % (2523960)Instructions burned: 1188 (million)
% 11.51/8.07 % (2524015)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=721798821:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 11.51/8.07 % (2524039)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=3592096530:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 11.51/8.07 % (2524015)Instruction limit reached!
% 11.51/8.07 % (2524015)------------------------------
% 11.51/8.07 % (2524015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2524015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2524015)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2524015)Termination reason: Instruction limit
% 11.51/8.07 % (2524015)Termination phase: Saturation
% 11.51/8.07 % (2524015)Time elapsed: 0.108 s
% 11.51/8.07 % (2524015)Peak memory usage: 94 MB
% 11.51/8.07 % (2524015)Instructions burned: 317 (million)
% 11.51/8.07 % (2524042)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2822862350:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 11.51/8.07 % (2523985)Instruction limit reached!
% 11.51/8.07 % (2523985)------------------------------
% 11.51/8.07 % (2523985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2523985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2523985)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2523985)Termination reason: Instruction limit
% 11.51/8.07 % (2523985)Termination phase: Saturation
% 11.51/8.07 % (2523985)Time elapsed: 0.743 s
% 11.51/8.07 % (2523985)Peak memory usage: 141 MB
% 11.51/8.07 % (2523985)Instructions burned: 2053 (million)
% 11.51/8.07 % (2524044)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2995676343:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2989 on theBenchmark for (2989ds/14534Mi)
% 11.51/8.07 % (2524039)First to succeed.
% 11.51/8.07 % (2524039)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2523936"
% 11.51/8.07 % (2524042)Instruction limit reached!
% 11.51/8.07 % (2524042)------------------------------
% 11.51/8.07 % (2524042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.51/8.07 % (2524042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.51/8.07 % (2524042)CaDiCaL version: 2.1.3
% 11.51/8.07 % (2524042)Termination reason: Instruction limit
% 11.51/8.07 % (2524042)Termination phase: Saturation
% 11.51/8.07 % (2524042)Time elapsed: 0.866 s
% 11.51/8.07 % (2524042)Peak memory usage: 122 MB
% 11.51/8.07 % (2524042)Instructions burned: 2836 (million)
% 11.51/8.07 % (2524039)Refutation found. Thanks to Tanya!
% 11.51/8.07 % SZS status Unsatisfiable for theBenchmark
% 11.51/8.07 % SZS output start Proof for theBenchmark
% See solution above
% 11.96/8.17 % (2524039)------------------------------
% 11.96/8.17 % (2524039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/8.17 % (2524039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/8.17 % (2524039)CaDiCaL version: 2.1.3
% 11.96/8.17 % (2524039)Termination reason: Refutation
% 11.96/8.17 % (2524039)Time elapsed: 0.874 s
% 11.96/8.17 % (2524039)Peak memory usage: 145 MB
% 11.96/8.17 % (2524039)Instructions burned: 2544 (million)
% 11.96/8.17 % (2524039)------------------------------
% 11.96/8.17 % (2524039)------------------------------
% 11.96/8.17 % (2523936)Success in time 1.674 s
% 11.96/8.17 % Vampire exiting
%------------------------------------------------------------------------------