%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:51:35 PM UTC 2026
% Result : Theorem 12.86s 2.15s
% Output : Proof 12.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 20
% Syntax : Number of formulae : 310 ( 305 unt; 0 def)
% Number of atoms : 319 ( 311 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 417 ( 26 sgn 92 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f8_nnf,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t22,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t49,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t22]) ).
fof(f16,axiom,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
fof(f16_nnf,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0] : multiplication(X0,coantidomain(X0)) = zero,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
multiplication(X0,coantidomain(X0)) = zero,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t11,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t40,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(orient,[status(thm)],[t11]) ).
fof(f17,axiom,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
fof(f17_nnf,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X0,X1] : addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c18,plain,
addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t26,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t80,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(orient,[status(thm)],[t26]) ).
fof(f19,axiom,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
fof(f19_nnf,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X0] : codomain(X0) = coantidomain(coantidomain(X0)),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c20,plain,
codomain(X0) = coantidomain(coantidomain(X0)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t10,plain,
coantidomain(coantidomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t109,plain,
coantidomain(coantidomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t18823,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(codomain(X1),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(step,[status(thm)],[t80,t109]) ).
cnf(t18824,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(codomain(X1),X2))) = coantidomain(multiplication(codomain(X1),X2)),
inference(step,[status(thm)],[t18823,t109]) ).
cnf(t113,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(codomain(X1),X2))) = coantidomain(multiplication(codomain(X1),X2)),
inference(rw,[status(thm)],[t18824]) ).
cnf(t17212,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(codomain(X1),X2))) = coantidomain(multiplication(codomain(X1),X2)),
inference(orient,[status(thm)],[t113]) ).
fof(f12,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t12,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t57,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t12]) ).
cnf(t17365,plain,
coantidomain(multiplication(codomain(antidomain(X1)),X1)) = addition(coantidomain(zero),coantidomain(multiplication(codomain(antidomain(X1)),X1))),
inference(cp,[status(thm)],[t17212,t57]) ).
fof(f6,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f6_nnf,plain,
! [A] : multiplication(one,A) = A,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : multiplication(one,A) = A,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t7,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t28,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t42,plain,
zero = coantidomain(one),
inference(cp,[status(thm)],[t40,t28]) ).
cnf(t149,plain,
coantidomain(one) = zero,
inference(orient,[status(thm)],[t42]) ).
cnf(t150,plain,
codomain(one) = coantidomain(zero),
inference(cp,[status(thm)],[t109,t149]) ).
cnf(t153,plain,
coantidomain(zero) = codomain(one),
inference(orient,[status(thm)],[t150]) ).
fof(f18,axiom,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
fof(f18_nnf,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X0] : addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c19,plain,
addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t16,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c19]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f0_nnf,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t13,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t66,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t18820,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(step,[status(thm)],[t16,t66]) ).
cnf(t91,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(orient,[status(thm)],[t18820]) ).
cnf(t18822,plain,
addition(coantidomain(X1),codomain(X1)) = one,
inference(step,[status(thm)],[t91,t109]) ).
cnf(t112,plain,
addition(coantidomain(X1),codomain(X1)) = one,
inference(rw,[status(thm)],[t18822]) ).
cnf(t18831,plain,
addition(codomain(X1),coantidomain(X1)) = one,
inference(step,[status(thm)],[t112,t66]) ).
cnf(t182,plain,
addition(codomain(X1),coantidomain(X1)) = one,
inference(orient,[status(thm)],[t18831]) ).
cnf(t186,plain,
one = addition(codomain(one),zero),
inference(cp,[status(thm)],[t182,t149]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f2_nnf,plain,
! [A] : addition(A,zero) = A,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] : addition(A,zero) = A,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t30,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t18832,plain,
one = codomain(one),
inference(step,[status(thm)],[t186,t30]) ).
cnf(t190,plain,
codomain(one) = one,
inference(orient,[status(thm)],[t18832]) ).
cnf(t18833,plain,
coantidomain(zero) = one,
inference(step,[status(thm)],[t153,t190]) ).
cnf(t191,plain,
coantidomain(zero) = one,
inference(orient,[status(thm)],[t18833]) ).
cnf(t19332,plain,
coantidomain(multiplication(codomain(antidomain(X1)),X1)) = addition(one,coantidomain(multiplication(codomain(antidomain(X1)),X1))),
inference(step,[status(thm)],[t17365,t191]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t19,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t32,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t18,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t141,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t18]) ).
fof(f1,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f1_nnf,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t17,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t71,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
fof(f3,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f3_nnf,plain,
! [A] : addition(A,A) = A,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : addition(A,A) = A,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t29,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t74,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t71,t29]) ).
cnf(t219,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t74]) ).
cnf(t226,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t141,t219]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t18847,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t226,t31]) ).
cnf(t235,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t18847]) ).
cnf(t241,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t235,t66]) ).
cnf(t248,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t241]) ).
cnf(t250,plain,
true = leq(coantidomain(X1),one),
inference(cp,[status(thm)],[t248,t182]) ).
cnf(t260,plain,
leq(coantidomain(X1),one) = true,
inference(orient,[status(thm)],[t250]) ).
cnf(t261,plain,
one = ifeq(true,true,addition(coantidomain(X1),one),one),
inference(cp,[status(thm)],[t32,t260]) ).
cnf(t18850,plain,
one = addition(coantidomain(X1),one),
inference(step,[status(thm)],[t261,t31]) ).
cnf(t18851,plain,
one = addition(one,coantidomain(X1)),
inference(step,[status(thm)],[t18850,t66]) ).
cnf(t267,plain,
addition(one,coantidomain(X1)) = one,
inference(orient,[status(thm)],[t18851]) ).
cnf(t19333,plain,
coantidomain(multiplication(codomain(antidomain(X1)),X1)) = one,
inference(step,[status(thm)],[t19332,t267]) ).
cnf(t17473,plain,
coantidomain(multiplication(codomain(antidomain(X1)),X1)) = one,
inference(orient,[status(thm)],[t19333]) ).
cnf(t17482,plain,
zero = multiplication(multiplication(codomain(antidomain(X1)),X1),one),
inference(cp,[status(thm)],[t40,t17473]) ).
fof(f4,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f4_nnf,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t20,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t35,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t20]) ).
cnf(t19334,plain,
zero = multiplication(codomain(antidomain(X1)),multiplication(X1,one)),
inference(step,[status(thm)],[t17482,t35]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f5_nnf,plain,
! [A] : multiplication(A,one) = A,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : multiplication(A,one) = A,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t27,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t19335,plain,
zero = multiplication(codomain(antidomain(X1)),X1),
inference(step,[status(thm)],[t19334,t27]) ).
cnf(t17513,plain,
multiplication(codomain(antidomain(X1)),X1) = zero,
inference(orient,[status(thm)],[t19335]) ).
cnf(t17517,plain,
multiplication(addition(codomain(antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(cp,[status(thm)],[t49,t17513]) ).
cnf(t67,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t66,t30]) ).
cnf(t157,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t67]) ).
cnf(t19341,plain,
multiplication(addition(codomain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(step,[status(thm)],[t17517,t157]) ).
cnf(t17856,plain,
multiplication(addition(codomain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(orient,[status(thm)],[t19341]) ).
cnf(t17866,plain,
multiplication(coantidomain(antidomain(X1)),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t17856,t182]) ).
cnf(t19342,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(step,[status(thm)],[t17866,t28]) ).
cnf(t17917,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(orient,[status(thm)],[t19342]) ).
fof(f15,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f15_nnf,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c16,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t9,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t114,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t115,plain,
domain(antidomain(X1)) = antidomain(domain(X1)),
inference(cp,[status(thm)],[t114,t114]) ).
cnf(t169,plain,
antidomain(domain(X1)) = domain(antidomain(X1)),
inference(orient,[status(thm)],[t115]) ).
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t21,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t36,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t21]) ).
cnf(t39,plain,
multiplication(X1,X2) = ifeq(leq(multiplication(X1,X3),multiplication(X1,X2)),true,multiplication(X1,addition(X3,X2)),multiplication(X1,X2)),
inference(cp,[status(thm)],[t32,t36]) ).
cnf(t657,plain,
ifeq(leq(multiplication(X1,X2),multiplication(X1,X3)),true,multiplication(X1,addition(X2,X3)),multiplication(X1,X3)) = multiplication(X1,X3),
inference(orient,[status(thm)],[t39]) ).
cnf(t675,plain,
multiplication(antidomain(X1),X2) = ifeq(leq(zero,multiplication(antidomain(X1),X2)),true,multiplication(antidomain(X1),addition(X1,X2)),multiplication(antidomain(X1),X2)),
inference(cp,[status(thm)],[t657,t57]) ).
cnf(t159,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t141,t157]) ).
cnf(t18830,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t159,t31]) ).
cnf(t160,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t18830]) ).
cnf(t19004,plain,
multiplication(antidomain(X1),X2) = ifeq(true,true,multiplication(antidomain(X1),addition(X1,X2)),multiplication(antidomain(X1),X2)),
inference(step,[status(thm)],[t675,t160]) ).
cnf(t19005,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X1,X2)),
inference(step,[status(thm)],[t19004,t31]) ).
cnf(t2352,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t19005]) ).
fof(f14,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t15,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t18821,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t15,t66]) ).
cnf(t106,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t18821]) ).
cnf(t18825,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t106,t114]) ).
cnf(t117,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[t18825]) ).
cnf(t18837,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t117,t66]) ).
cnf(t206,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t18837]) ).
cnf(t2356,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),one),
inference(cp,[status(thm)],[t2352,t206]) ).
cnf(t19006,plain,
multiplication(domain(antidomain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),one),
inference(step,[status(thm)],[t2356,t169]) ).
cnf(t60,plain,
multiplication(addition(X1,antidomain(X2)),X2) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t49,t57]) ).
cnf(t18875,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(step,[status(thm)],[t60,t30]) ).
cnf(t540,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(orient,[status(thm)],[t18875]) ).
cnf(t541,plain,
multiplication(domain(X1),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t540,t206]) ).
cnf(t18876,plain,
multiplication(domain(X1),X1) = X1,
inference(step,[status(thm)],[t541,t28]) ).
cnf(t556,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t18876]) ).
cnf(t19007,plain,
antidomain(X1) = multiplication(antidomain(domain(X1)),one),
inference(step,[status(thm)],[t19006,t556]) ).
cnf(t19008,plain,
antidomain(X1) = antidomain(domain(X1)),
inference(step,[status(thm)],[t19007,t27]) ).
cnf(t19009,plain,
antidomain(X1) = domain(antidomain(X1)),
inference(step,[status(thm)],[t19008,t169]) ).
cnf(t2370,plain,
domain(antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t19009]) ).
cnf(t19010,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(step,[status(thm)],[t169,t2370]) ).
cnf(t2371,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t19010]) ).
cnf(t17918,plain,
domain(X1) = multiplication(coantidomain(antidomain(X1)),domain(X1)),
inference(cp,[status(thm)],[t17917,t2371]) ).
cnf(t111,plain,
zero = multiplication(coantidomain(X1),codomain(X1)),
inference(cp,[status(thm)],[t40,t109]) ).
cnf(t171,plain,
multiplication(coantidomain(X1),codomain(X1)) = zero,
inference(orient,[status(thm)],[t111]) ).
cnf(t178,plain,
multiplication(coantidomain(X1),addition(X2,codomain(X1))) = addition(multiplication(coantidomain(X1),X2),zero),
inference(cp,[status(thm)],[t36,t171]) ).
cnf(t19148,plain,
multiplication(coantidomain(X1),addition(X2,codomain(X1))) = multiplication(coantidomain(X1),X2),
inference(step,[status(thm)],[t178,t30]) ).
cnf(t7797,plain,
multiplication(coantidomain(X1),addition(X2,codomain(X1))) = multiplication(coantidomain(X1),X2),
inference(orient,[status(thm)],[t19148]) ).
cnf(t213,plain,
addition(domain(X1),addition(antidomain(X1),X2)) = addition(one,X2),
inference(cp,[status(thm)],[t71,t206]) ).
cnf(t2944,plain,
addition(domain(X1),addition(antidomain(X1),X2)) = addition(one,X2),
inference(orient,[status(thm)],[t213]) ).
cnf(t52,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t28]) ).
cnf(t405,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t52]) ).
cnf(t44,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t36,t40]) ).
cnf(t18872,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(step,[status(thm)],[t44,t30]) ).
cnf(t500,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(orient,[status(thm)],[t18872]) ).
cnf(t502,plain,
multiplication(X1,codomain(X1)) = multiplication(X1,one),
inference(cp,[status(thm)],[t500,t182]) ).
cnf(t18873,plain,
multiplication(X1,codomain(X1)) = X1,
inference(step,[status(thm)],[t502,t27]) ).
cnf(t517,plain,
multiplication(X1,codomain(X1)) = X1,
inference(orient,[status(thm)],[t18873]) ).
cnf(t519,plain,
multiplication(addition(one,X1),codomain(X1)) = addition(codomain(X1),X1),
inference(cp,[status(thm)],[t405,t517]) ).
cnf(t18965,plain,
multiplication(addition(one,X1),codomain(X1)) = addition(X1,codomain(X1)),
inference(step,[status(thm)],[t519,t66]) ).
cnf(t1931,plain,
multiplication(addition(one,X1),codomain(X1)) = addition(X1,codomain(X1)),
inference(orient,[status(thm)],[t18965]) ).
cnf(t249,plain,
true = leq(antidomain(X1),one),
inference(cp,[status(thm)],[t248,t206]) ).
cnf(t256,plain,
leq(antidomain(X1),one) = true,
inference(orient,[status(thm)],[t249]) ).
cnf(t257,plain,
one = ifeq(true,true,addition(antidomain(X1),one),one),
inference(cp,[status(thm)],[t32,t256]) ).
cnf(t18848,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t257,t31]) ).
cnf(t18849,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t18848,t66]) ).
cnf(t263,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t18849]) ).
cnf(t1940,plain,
addition(antidomain(X1),codomain(antidomain(X1))) = multiplication(one,codomain(antidomain(X1))),
inference(cp,[status(thm)],[t1931,t263]) ).
cnf(t18966,plain,
addition(antidomain(X1),codomain(antidomain(X1))) = codomain(antidomain(X1)),
inference(step,[status(thm)],[t1940,t28]) ).
cnf(t1958,plain,
addition(antidomain(X1),codomain(antidomain(X1))) = codomain(antidomain(X1)),
inference(orient,[status(thm)],[t18966]) ).
cnf(t2947,plain,
addition(one,codomain(antidomain(X1))) = addition(domain(X1),codomain(antidomain(X1))),
inference(cp,[status(thm)],[t2944,t1958]) ).
cnf(t222,plain,
addition(codomain(X1),coantidomain(X1)) = addition(codomain(X1),one),
inference(cp,[status(thm)],[t219,t182]) ).
cnf(t18845,plain,
one = addition(codomain(X1),one),
inference(step,[status(thm)],[t222,t182]) ).
cnf(t18846,plain,
one = addition(one,codomain(X1)),
inference(step,[status(thm)],[t18845,t66]) ).
cnf(t231,plain,
addition(one,codomain(X1)) = one,
inference(orient,[status(thm)],[t18846]) ).
cnf(t19031,plain,
one = addition(domain(X1),codomain(antidomain(X1))),
inference(step,[status(thm)],[t2947,t231]) ).
cnf(t2966,plain,
addition(domain(X1),codomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t19031]) ).
cnf(t7801,plain,
multiplication(coantidomain(antidomain(X1)),domain(X1)) = multiplication(coantidomain(antidomain(X1)),one),
inference(cp,[status(thm)],[t7797,t2966]) ).
cnf(t19150,plain,
multiplication(coantidomain(antidomain(X1)),domain(X1)) = coantidomain(antidomain(X1)),
inference(step,[status(thm)],[t7801,t27]) ).
cnf(t7842,plain,
multiplication(coantidomain(antidomain(X1)),domain(X1)) = coantidomain(antidomain(X1)),
inference(orient,[status(thm)],[t19150]) ).
cnf(t19343,plain,
domain(X1) = coantidomain(antidomain(X1)),
inference(step,[status(thm)],[t17918,t7842]) ).
cnf(t17959,plain,
coantidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t19343]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f13,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi14,axiom,
addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t23,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi14]) ).
cnf(t18829,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = true,
inference(step,[status(thm)],[t23,t114]) ).
cnf(t130,plain,
leq(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,domain(X2)))) = true,
inference(orient,[status(thm)],[t18829]) ).
cnf(t133,plain,
true = leq(antidomain(zero),antidomain(multiplication(X1,domain(coantidomain(X1))))),
inference(cp,[status(thm)],[t130,t40]) ).
cnf(t58,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t57,t27]) ).
cnf(t151,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t58]) ).
cnf(t152,plain,
domain(one) = antidomain(zero),
inference(cp,[status(thm)],[t114,t151]) ).
cnf(t155,plain,
antidomain(zero) = domain(one),
inference(orient,[status(thm)],[t152]) ).
cnf(t210,plain,
one = addition(domain(one),zero),
inference(cp,[status(thm)],[t206,t151]) ).
cnf(t18838,plain,
one = domain(one),
inference(step,[status(thm)],[t210,t30]) ).
cnf(t214,plain,
domain(one) = one,
inference(orient,[status(thm)],[t18838]) ).
cnf(t18839,plain,
antidomain(zero) = one,
inference(step,[status(thm)],[t155,t214]) ).
cnf(t215,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t18839]) ).
cnf(t19368,plain,
true = leq(one,antidomain(multiplication(X1,domain(coantidomain(X1))))),
inference(step,[status(thm)],[t133,t215]) ).
cnf(t18407,plain,
leq(one,antidomain(multiplication(X1,domain(coantidomain(X1))))) = true,
inference(orient,[status(thm)],[t19368]) ).
cnf(t18411,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = ifeq(true,true,addition(one,antidomain(multiplication(X1,domain(coantidomain(X1))))),antidomain(multiplication(X1,domain(coantidomain(X1))))),
inference(cp,[status(thm)],[t32,t18407]) ).
cnf(t19369,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = addition(one,antidomain(multiplication(X1,domain(coantidomain(X1))))),
inference(step,[status(thm)],[t18411,t31]) ).
cnf(t19370,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = one,
inference(step,[status(thm)],[t19369,t263]) ).
cnf(t18414,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = one,
inference(orient,[status(thm)],[t19370]) ).
cnf(t18426,plain,
zero = multiplication(one,multiplication(X1,domain(coantidomain(X1)))),
inference(cp,[status(thm)],[t57,t18414]) ).
cnf(t19371,plain,
zero = multiplication(X1,domain(coantidomain(X1))),
inference(step,[status(thm)],[t18426,t28]) ).
cnf(t18448,plain,
multiplication(X1,domain(coantidomain(X1))) = zero,
inference(orient,[status(thm)],[t19371]) ).
cnf(t18455,plain,
multiplication(X1,addition(domain(coantidomain(X1)),X2)) = addition(zero,multiplication(X1,X2)),
inference(cp,[status(thm)],[t36,t18448]) ).
cnf(t19378,plain,
multiplication(X1,addition(domain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(step,[status(thm)],[t18455,t157]) ).
cnf(t18683,plain,
multiplication(X1,addition(domain(coantidomain(X1)),X2)) = multiplication(X1,X2),
inference(orient,[status(thm)],[t19378]) ).
cnf(t18687,plain,
multiplication(X1,antidomain(coantidomain(X1))) = multiplication(X1,one),
inference(cp,[status(thm)],[t18683,t206]) ).
cnf(t19379,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(step,[status(thm)],[t18687,t27]) ).
cnf(t18729,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(orient,[status(thm)],[t19379]) ).
cnf(t110,plain,
codomain(coantidomain(X1)) = coantidomain(codomain(X1)),
inference(cp,[status(thm)],[t109,t109]) ).
cnf(t167,plain,
coantidomain(codomain(X1)) = codomain(coantidomain(X1)),
inference(orient,[status(thm)],[t110]) ).
cnf(t50,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = addition(zero,multiplication(X2,coantidomain(X1))),
inference(cp,[status(thm)],[t49,t40]) ).
cnf(t18972,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(step,[status(thm)],[t50,t157]) ).
cnf(t2045,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(orient,[status(thm)],[t18972]) ).
cnf(t2049,plain,
multiplication(coantidomain(X1),coantidomain(codomain(X1))) = multiplication(one,coantidomain(codomain(X1))),
inference(cp,[status(thm)],[t2045,t182]) ).
cnf(t18973,plain,
multiplication(coantidomain(X1),codomain(coantidomain(X1))) = multiplication(one,coantidomain(codomain(X1))),
inference(step,[status(thm)],[t2049,t167]) ).
cnf(t18974,plain,
coantidomain(X1) = multiplication(one,coantidomain(codomain(X1))),
inference(step,[status(thm)],[t18973,t517]) ).
cnf(t18975,plain,
coantidomain(X1) = coantidomain(codomain(X1)),
inference(step,[status(thm)],[t18974,t28]) ).
cnf(t18976,plain,
coantidomain(X1) = codomain(coantidomain(X1)),
inference(step,[status(thm)],[t18975,t167]) ).
cnf(t2069,plain,
codomain(coantidomain(X1)) = coantidomain(X1),
inference(orient,[status(thm)],[t18976]) ).
cnf(t18977,plain,
coantidomain(codomain(X1)) = coantidomain(X1),
inference(step,[status(thm)],[t167,t2069]) ).
cnf(t2070,plain,
coantidomain(codomain(X1)) = coantidomain(X1),
inference(orient,[status(thm)],[t18977]) ).
cnf(t18731,plain,
codomain(X1) = multiplication(codomain(X1),antidomain(coantidomain(X1))),
inference(cp,[status(thm)],[t18729,t2070]) ).
cnf(t116,plain,
zero = multiplication(domain(X1),antidomain(X1)),
inference(cp,[status(thm)],[t57,t114]) ).
cnf(t195,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(orient,[status(thm)],[t116]) ).
cnf(t200,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),zero),
inference(cp,[status(thm)],[t49,t195]) ).
cnf(t19155,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(step,[status(thm)],[t200,t30]) ).
cnf(t7974,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(orient,[status(thm)],[t19155]) ).
cnf(t189,plain,
addition(codomain(X1),addition(coantidomain(X1),X2)) = addition(one,X2),
inference(cp,[status(thm)],[t71,t182]) ).
cnf(t2704,plain,
addition(codomain(X1),addition(coantidomain(X1),X2)) = addition(one,X2),
inference(orient,[status(thm)],[t189]) ).
cnf(t37,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t36,t27]) ).
cnf(t336,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t37]) ).
cnf(t557,plain,
multiplication(domain(X1),addition(one,X1)) = addition(domain(X1),X1),
inference(cp,[status(thm)],[t336,t556]) ).
cnf(t18971,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(step,[status(thm)],[t557,t66]) ).
cnf(t2014,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t18971]) ).
cnf(t2026,plain,
addition(coantidomain(X1),domain(coantidomain(X1))) = multiplication(domain(coantidomain(X1)),one),
inference(cp,[status(thm)],[t2014,t267]) ).
cnf(t18988,plain,
addition(coantidomain(X1),domain(coantidomain(X1))) = domain(coantidomain(X1)),
inference(step,[status(thm)],[t2026,t27]) ).
cnf(t2153,plain,
addition(coantidomain(X1),domain(coantidomain(X1))) = domain(coantidomain(X1)),
inference(orient,[status(thm)],[t18988]) ).
cnf(t2707,plain,
addition(one,domain(coantidomain(X1))) = addition(codomain(X1),domain(coantidomain(X1))),
inference(cp,[status(thm)],[t2704,t2153]) ).
cnf(t221,plain,
addition(domain(X1),antidomain(X1)) = addition(domain(X1),one),
inference(cp,[status(thm)],[t219,t206]) ).
cnf(t18843,plain,
one = addition(domain(X1),one),
inference(step,[status(thm)],[t221,t206]) ).
cnf(t18844,plain,
one = addition(one,domain(X1)),
inference(step,[status(thm)],[t18843,t66]) ).
cnf(t227,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t18844]) ).
cnf(t19029,plain,
one = addition(codomain(X1),domain(coantidomain(X1))),
inference(step,[status(thm)],[t2707,t227]) ).
cnf(t2919,plain,
addition(codomain(X1),domain(coantidomain(X1))) = one,
inference(orient,[status(thm)],[t19029]) ).
cnf(t7978,plain,
multiplication(codomain(X1),antidomain(coantidomain(X1))) = multiplication(one,antidomain(coantidomain(X1))),
inference(cp,[status(thm)],[t7974,t2919]) ).
cnf(t19157,plain,
multiplication(codomain(X1),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(step,[status(thm)],[t7978,t28]) ).
cnf(t8029,plain,
multiplication(codomain(X1),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(orient,[status(thm)],[t19157]) ).
cnf(t19380,plain,
codomain(X1) = antidomain(coantidomain(X1)),
inference(step,[status(thm)],[t18731,t8029]) ).
cnf(t18756,plain,
antidomain(coantidomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t19380]) ).
cnf(t18758,plain,
domain(coantidomain(X1)) = coantidomain(codomain(X1)),
inference(cp,[status(thm)],[t17959,t18756]) ).
cnf(t19384,plain,
domain(coantidomain(X1)) = coantidomain(X1),
inference(step,[status(thm)],[t18758,t2070]) ).
cnf(t18807,plain,
domain(coantidomain(X1)) = coantidomain(X1),
inference(orient,[status(thm)],[t19384]) ).
fof(f20,conjecture,
! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0] : domain(coantidomain(X0)) = coantidomain(X0),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0] : domain(coantidomain(X0)) != coantidomain(X0),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
domain(coantidomain(sk0)) != coantidomain(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f20_nnf]) ).
cnf(c21,plain,
domain(coantidomain(sk0)) != coantidomain(sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
domain(coantidomain(sk0)) != coantidomain(sk0),
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
coantidomain(sk0) != coantidomain(sk0),
inference(rw,[status(thm)],[goal_0,t18807]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE092+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 18:57:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.86/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.86/2.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------