%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 11:52:13 AM UTC 2026
% Result : Unsatisfiable 17.33s 3.75s
% Output : Refutation 20.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 101
% Number of leaves : 6
% Syntax : Number of formulae : 135 ( 135 unt; 0 def)
% Number of atoms : 135 ( 134 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 357 ( 357 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f3,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
fof(f5,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
fof(f7,plain,
! [X0] : true = is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
fof(f9,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_47) ).
fof(f11,plain,
true != is_a_theorem(implies(implies(x,not(y)),implies(y,not(x)))),
inference(reorient_equations,[],[f10]) ).
fof(f13,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f5]) ).
fof(f15,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
inference(superposition,[],[f3,f9]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),X3)),true,ifeq(true,true,is_a_theorem(X3),true),true),
inference(superposition,[],[f3,f5]) ).
fof(f22,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),X3)),true,is_a_theorem(X3),true),
inference(forward_demodulation,[],[f16,f1]) ).
fof(f23,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,is_a_theorem(X2),true),
inference(forward_demodulation,[],[f15,f1]) ).
fof(f25,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f13,f1]) ).
fof(f27,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f25,f9]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),true),
inference(superposition,[],[f25,f5]) ).
fof(f29,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),true),
inference(superposition,[],[f25,f7]) ).
fof(f34,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(forward_demodulation,[],[f29,f1]) ).
fof(f35,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X0,X2)),X3),implies(implies(X0,X1),X3))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f36,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f48,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),true),
inference(superposition,[],[f3,f35]) ).
fof(f52,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),true,is_a_theorem(implies(implies(X2,X0),X3)),true),
inference(forward_demodulation,[],[f48,f1]) ).
fof(f55,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),true),
inference(superposition,[],[f52,f35]) ).
fof(f69,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(X0,X1)),implies(implies(X2,X0),implies(X3,implies(X2,X1))))),
inference(forward_demodulation,[],[f55,f1]) ).
fof(f86,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),true),
inference(superposition,[],[f3,f36]) ).
fof(f88,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f52,f36]) ).
fof(f95,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,not(X0)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f96,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(not(X0),X1),X2)),true,is_a_theorem(implies(X0,X2)),true),
inference(forward_demodulation,[],[f86,f1]) ).
fof(f100,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),true),
inference(superposition,[],[f3,f69]) ).
fof(f110,plain,
! [X2,X3,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X3,X1),implies(X0,implies(X3,X2)))),true),
inference(forward_demodulation,[],[f100,f1]) ).
fof(f114,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f110,f34]) ).
fof(f132,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X0),X0)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f114,f1]) ).
fof(f139,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),true),
inference(superposition,[],[f3,f132]) ).
fof(f147,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(implies(X1,X2),implies(X0,X2))),true),
inference(forward_demodulation,[],[f139,f1]) ).
fof(f283,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),true),
inference(superposition,[],[f96,f95]) ).
fof(f285,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(X0,X0)),true),
inference(superposition,[],[f96,f7]) ).
fof(f299,plain,
! [X0] : true = is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[],[f285,f1]) ).
fof(f301,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(forward_demodulation,[],[f283,f1]) ).
fof(f326,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,ifeq(true,true,is_a_theorem(X1),true),true),
inference(superposition,[],[f3,f299]) ).
fof(f327,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(X1),true),
inference(forward_demodulation,[],[f326,f1]) ).
fof(f373,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),true),
inference(superposition,[],[f327,f301]) ).
fof(f390,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(not(implies(X0,X0)),X2))),
inference(forward_demodulation,[],[f373,f1]) ).
fof(f401,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f147,f390]) ).
fof(f436,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f401,f1]) ).
fof(f448,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(implies(X2,X1)),true),true),
inference(superposition,[],[f3,f436]) ).
fof(f463,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X0),X1)),true,is_a_theorem(implies(X2,X1)),true),
inference(forward_demodulation,[],[f448,f1]) ).
fof(f699,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),true),
inference(superposition,[],[f463,f34]) ).
fof(f749,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(implies(not(X0),X0),X0))),
inference(forward_demodulation,[],[f699,f1]) ).
fof(f757,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f110,f749]) ).
fof(f789,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X1),X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f757,f1]) ).
fof(f803,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X2,implies(X0,X1))),true),true),
inference(superposition,[],[f3,f789]) ).
fof(f807,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),true),
inference(superposition,[],[f52,f789]) ).
fof(f816,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(not(X1),X0),implies(X2,implies(implies(X0,X1),X1)))),
inference(forward_demodulation,[],[f807,f1]) ).
fof(f819,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X1))),true,is_a_theorem(implies(X2,implies(X0,X1))),true),
inference(forward_demodulation,[],[f803,f1]) ).
fof(f966,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f96,f816]) ).
fof(f978,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X0,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f966,f1]) ).
fof(f987,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X1,X0),X0),X2),implies(X0,X2))),true),
inference(superposition,[],[f147,f978]) ).
fof(f1020,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X1,X0),X0),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f987,f1]) ).
fof(f1039,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X1,implies(X2,X1)))),true),
inference(superposition,[],[f52,f1020]) ).
fof(f1050,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X1,implies(X2,X1)))),
inference(forward_demodulation,[],[f1039,f1]) ).
fof(f1072,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X0,X1))),true),
inference(superposition,[],[f23,f1050]) ).
fof(f1088,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(X0,X1))),
inference(forward_demodulation,[],[f1072,f1]) ).
fof(f1104,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),true),
inference(superposition,[],[f25,f1088]) ).
fof(f1128,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1104,f1]) ).
fof(f1249,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),true),
inference(superposition,[],[f3,f1128]) ).
fof(f1265,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(implies(X0,X1),X2)),true,is_a_theorem(implies(X1,X2)),true),
inference(forward_demodulation,[],[f1249,f1]) ).
fof(f1317,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),true),
inference(superposition,[],[f1265,f816]) ).
fof(f1405,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X0),X0)))),
inference(forward_demodulation,[],[f1317,f1]) ).
fof(f1416,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),true),
inference(superposition,[],[f147,f1405]) ).
fof(f1452,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(forward_demodulation,[],[f1416,f1]) ).
fof(f1473,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),true),
inference(superposition,[],[f52,f1452]) ).
fof(f1484,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X0,X1)),implies(X0,implies(X2,X1)))),
inference(forward_demodulation,[],[f1473,f1]) ).
fof(f1509,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),true),
inference(superposition,[],[f3,f1484]) ).
fof(f1510,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true),
inference(superposition,[],[f23,f1484]) ).
fof(f1528,plain,
! [X0,X1] : true = is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(forward_demodulation,[],[f1510,f1]) ).
fof(f1529,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),
inference(forward_demodulation,[],[f1509,f1]) ).
fof(f1545,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),true),
inference(superposition,[],[f25,f1528]) ).
fof(f1556,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(forward_demodulation,[],[f1545,f1]) ).
fof(f1725,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X2,implies(implies(implies(X0,X1),X0),X0))),true),
inference(superposition,[],[f819,f1556]) ).
fof(f1764,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(X2,implies(implies(implies(X0,X1),X0),X0))),
inference(forward_demodulation,[],[f1725,f1]) ).
fof(f1827,plain,
! [X3,X4] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X4),X3),X3)),true),
inference(superposition,[],[f22,f1764]) ).
fof(f1836,plain,
! [X3,X4] : true = is_a_theorem(implies(implies(implies(X3,X4),X3),X3)),
inference(forward_demodulation,[],[f1827,f1]) ).
fof(f1856,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),true),
inference(superposition,[],[f52,f1836]) ).
fof(f1878,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f1856,f1]) ).
fof(f1895,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X0,X1))),true,is_a_theorem(implies(X0,X1)),true),true),
inference(superposition,[],[f3,f1878]) ).
fof(f1913,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X0,X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f1895,f1]) ).
fof(f1938,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),true),
inference(superposition,[],[f1913,f816]) ).
fof(f1990,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(forward_demodulation,[],[f1938,f1]) ).
fof(f2191,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(not(X0),X1),X0))),true),
inference(superposition,[],[f1529,f1990]) ).
fof(f2225,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(not(X0),X1),X0))),
inference(forward_demodulation,[],[f2191,f1]) ).
fof(f2233,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(not(X1),X0)),implies(implies(X0,X1),implies(X2,X1)))),true),
inference(superposition,[],[f110,f2225]) ).
fof(f2267,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(not(X1),X0)),implies(implies(X0,X1),implies(X2,X1)))),
inference(forward_demodulation,[],[f2233,f1]) ).
fof(f2322,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(not(X1),X2))),true,is_a_theorem(implies(implies(X2,X1),implies(X0,X1))),true),true),
inference(superposition,[],[f3,f2267]) ).
fof(f2348,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(not(X1),X2))),true,is_a_theorem(implies(implies(X2,X1),implies(X0,X1))),true),
inference(forward_demodulation,[],[f2322,f1]) ).
fof(f2675,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X0,X1),X2),X0))),true),
inference(superposition,[],[f2348,f1556]) ).
fof(f2763,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X0,X1),X2),X0))),
inference(forward_demodulation,[],[f2675,f1]) ).
fof(f2781,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,X2),X0),implies(implies(X0,X1),X1))),true),
inference(superposition,[],[f1529,f2763]) ).
fof(f2819,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(implies(X1,X2),X0),implies(implies(X0,X1),X1))),
inference(forward_demodulation,[],[f2781,f1]) ).
fof(f2842,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X2,X1),X0),X0))),true),
inference(superposition,[],[f52,f2819]) ).
fof(f2853,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,X0),implies(implies(implies(X2,X1),X0),X0))),
inference(forward_demodulation,[],[f2842,f1]) ).
fof(f2871,plain,
! [X2,X3,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X3,implies(implies(X0,X2),X1)),implies(implies(X0,X1),implies(X3,X1)))),true),
inference(superposition,[],[f110,f2853]) ).
fof(f2905,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(implies(implies(X3,implies(implies(X0,X2),X1)),implies(implies(X0,X1),implies(X3,X1)))),
inference(forward_demodulation,[],[f2871,f1]) ).
fof(f2973,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X0,X2)),implies(implies(X0,X1),implies(X0,X2)))),true),
inference(superposition,[],[f22,f2905]) ).
fof(f2984,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X1,implies(X0,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(forward_demodulation,[],[f2973,f1]) ).
fof(f3005,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X1,X0),implies(X1,X2))),true),true),
inference(superposition,[],[f3,f2984]) ).
fof(f3033,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(implies(X1,X0),implies(X1,X2))),true),
inference(forward_demodulation,[],[f3005,f1]) ).
fof(f3065,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(implies(X0,X0),X1)),implies(X2,X1))),true),
inference(superposition,[],[f3033,f436]) ).
fof(f3174,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(implies(X0,X0),X1)),implies(X2,X1))),
inference(forward_demodulation,[],[f3065,f1]) ).
fof(f3431,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(implies(X1,X1),X2))),true,is_a_theorem(implies(X0,X2)),true),true),
inference(superposition,[],[f3,f3174]) ).
fof(f3458,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(implies(X1,X1),X2))),true,is_a_theorem(implies(X0,X2)),true),
inference(forward_demodulation,[],[f3431,f1]) ).
fof(f3538,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X1)),implies(X0,X1))),true),
inference(superposition,[],[f3458,f2905]) ).
fof(f3681,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,implies(implies(X1,X2),X1)),implies(X0,X1))),
inference(forward_demodulation,[],[f3538,f1]) ).
fof(f3720,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(implies(X1,X2),X1))),true,is_a_theorem(implies(X0,X1)),true),true),
inference(superposition,[],[f3,f3681]) ).
fof(f3748,plain,
! [X2,X0,X1] : true = ifeq(is_a_theorem(implies(X0,implies(implies(X1,X2),X1))),true,is_a_theorem(implies(X0,X1)),true),
inference(forward_demodulation,[],[f3720,f1]) ).
fof(f3771,plain,
! [X0] : true = ifeq(true,true,is_a_theorem(implies(implies(X0,not(X0)),not(X0))),true),
inference(superposition,[],[f3748,f34]) ).
fof(f3917,plain,
! [X0] : true = is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(forward_demodulation,[],[f3771,f1]) ).
fof(f4519,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(not(X0),X1),implies(implies(X0,not(X0)),X1))),true),
inference(superposition,[],[f25,f3917]) ).
fof(f4543,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(not(X0),X1),implies(implies(X0,not(X0)),X1))),
inference(forward_demodulation,[],[f4519,f1]) ).
fof(f4907,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(X1,implies(implies(X0,not(X0)),not(X0)))),true),
inference(superposition,[],[f463,f4543]) ).
fof(f4940,plain,
! [X0,X1] : true = is_a_theorem(implies(X1,implies(implies(X0,not(X0)),not(X0)))),
inference(forward_demodulation,[],[f4907,f1]) ).
fof(f5007,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,not(X1)),implies(X0,not(X1)))),true),
inference(superposition,[],[f1529,f4940]) ).
fof(f5056,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,not(X1)),implies(X0,not(X1)))),
inference(forward_demodulation,[],[f5007,f1]) ).
fof(f5076,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,implies(X0,not(X0))),implies(X1,not(X0)))),true),
inference(superposition,[],[f3033,f5056]) ).
fof(f5124,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,implies(X0,not(X0))),implies(X1,not(X0)))),
inference(forward_demodulation,[],[f5076,f1]) ).
fof(f6588,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,X0),implies(implies(X0,not(X1)),not(X1)))),true),
inference(superposition,[],[f52,f5124]) ).
fof(f6597,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,X0),implies(implies(X0,not(X1)),not(X1)))),
inference(forward_demodulation,[],[f6588,f1]) ).
fof(f6626,plain,
! [X2,X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X2,implies(X1,not(X0))),implies(implies(X0,X1),implies(X2,not(X0))))),true),
inference(superposition,[],[f110,f6597]) ).
fof(f6675,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X2,implies(X1,not(X0))),implies(implies(X0,X1),implies(X2,not(X0))))),
inference(forward_demodulation,[],[f6626,f1]) ).
fof(f6710,plain,
! [X0,X1] : true = ifeq(true,true,is_a_theorem(implies(implies(X1,not(X0)),implies(X0,not(X1)))),true),
inference(superposition,[],[f23,f6675]) ).
fof(f6726,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X1,not(X0)),implies(X0,not(X1)))),
inference(forward_demodulation,[],[f6710,f1]) ).
fof(f6741,plain,
true != true,
inference(superposition,[],[f11,f6726]) ).
fof(f6787,plain,
$false,
inference(trivial_inequality_removal,[],[f6741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n011.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 15:38:45 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.33/3.75 % (2575411)Detected a unit-equality problem, will run specialized UEQ schedule.
% 17.33/3.75 % (2575416)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=1868788862:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 17.33/3.75 % (2575422)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1878994868:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 17.33/3.75 % (2575418)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2824981279:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 17.33/3.75 % (2575419)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3270466723:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 17.33/3.75 % (2575421)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3518114667:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 17.33/3.75 % (2575417)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=2891249096:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 17.33/3.75 % (2575420)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1448268712:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 17.33/3.75 % (2575419)Instruction limit reached!
% 17.33/3.75 % (2575419)------------------------------
% 17.33/3.75 % (2575419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575419)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575419)Termination reason: Instruction limit
% 17.33/3.75 % (2575419)Termination phase: Saturation
% 17.33/3.75 % (2575419)Time elapsed: 0.137 s
% 17.33/3.75 % (2575419)Peak memory usage: 89 MB
% 17.33/3.75 % (2575419)Instructions burned: 136 (million)
% 17.33/3.75 % (2575420)Instruction limit reached!
% 17.33/3.75 % (2575420)------------------------------
% 17.33/3.75 % (2575420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575420)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575420)Termination reason: Instruction limit
% 17.33/3.75 % (2575420)Termination phase: Saturation
% 17.33/3.75 % (2575420)Time elapsed: 0.180 s
% 17.33/3.75 % (2575420)Peak memory usage: 90 MB
% 17.33/3.75 % (2575420)Instructions burned: 181 (million)
% 17.33/3.75 % (2575421)Instruction limit reached!
% 17.33/3.75 % (2575421)------------------------------
% 17.33/3.75 % (2575421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575421)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575421)Termination reason: Instruction limit
% 17.33/3.75 % (2575421)Termination phase: Saturation
% 17.33/3.75 % (2575421)Time elapsed: 0.257 s
% 17.33/3.75 % (2575421)Peak memory usage: 91 MB
% 17.33/3.75 % (2575421)Instructions burned: 258 (million)
% 17.33/3.75 % (2575430)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=532095867:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 17.33/3.75 % (2575431)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=945523064:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 17.33/3.75 % (2575432)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3859331354:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 17.33/3.75 % (2575422)Instruction limit reached!
% 17.33/3.75 % (2575422)------------------------------
% 17.33/3.75 % (2575422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575422)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575422)Termination reason: Instruction limit
% 17.33/3.75 % (2575422)Termination phase: Saturation
% 17.33/3.75 % (2575422)Time elapsed: 0.544 s
% 17.33/3.75 % (2575422)Peak memory usage: 98 MB
% 17.33/3.75 % (2575422)Instructions burned: 1188 (million)
% 17.33/3.75 % (2575432)Instruction limit reached!
% 17.33/3.75 % (2575432)------------------------------
% 17.33/3.75 % (2575432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575432)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575432)Termination reason: Instruction limit
% 17.33/3.75 % (2575432)Termination phase: Saturation
% 17.33/3.75 % (2575432)Time elapsed: 0.191 s
% 17.33/3.75 % (2575432)Peak memory usage: 88 MB
% 17.33/3.75 % (2575432)Instructions burned: 215 (million)
% 17.33/3.75 % (2575438)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=3812061372:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 17.33/3.75 % (2575439)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=413931014:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 17.33/3.75 % (2575438)Instruction limit reached!
% 17.33/3.75 % (2575438)------------------------------
% 17.33/3.75 % (2575438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.33/3.75 % (2575438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.33/3.75 % (2575438)CaDiCaL version: 2.1.3
% 17.33/3.75 % (2575438)Termination reason: Instruction limit
% 17.33/3.75 % (2575438)Termination phase: Saturation
% 17.33/3.75 % (2575438)Time elapsed: 0.312 s
% 17.33/3.75 % (2575438)Peak memory usage: 93 MB
% 17.33/3.75 % (2575438)Instructions burned: 318 (million)
% 17.33/3.75 % (2575442)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=574286689:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 17.33/3.75 % (2575417)First to succeed.
% 17.33/3.75 % (2575417)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2575411"
% 17.33/3.75 % (2575430)Also succeeded, but the first one will report.
% 17.33/3.75 % (2575417)Refutation found. Thanks to Tanya!
% 17.33/3.75 % SZS status Unsatisfiable for theBenchmark
% 17.33/3.75 % SZS output start Proof for theBenchmark
% See solution above
% 20.62/3.99 % (2575417)------------------------------
% 20.62/3.99 % (2575417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.62/3.99 % (2575417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.62/3.99 % (2575417)CaDiCaL version: 2.1.3
% 20.62/3.99 % (2575417)Termination reason: Refutation
% 20.62/3.99 % (2575417)Time elapsed: 2.121 s
% 20.62/3.99 % (2575417)Peak memory usage: 138 MB
% 20.62/3.99 % (2575417)Instructions burned: 1965 (million)
% 20.62/3.99 % (2575417)------------------------------
% 20.62/3.99 % (2575417)------------------------------
% 20.62/3.99 % (2575411)Success in time 2.826 s
% 20.62/3.99 % Vampire exiting
%------------------------------------------------------------------------------