%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE091+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 : n020.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 15.79s 2.50s
% Output : Proof 15.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 18
% Syntax : Number of formulae : 241 ( 236 unt; 0 def)
% Number of atoms : 250 ( 242 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 : 325 ( 23 sgn 77 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
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]) ).
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(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(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(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]) ).
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(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(t159,plain,
true = ifeq(X1,X1,leq(zero,X1),true),
inference(cp,[status(thm)],[t141,t157]) ).
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(t18841,plain,
true = leq(zero,X1),
inference(step,[status(thm)],[t159,t31]) ).
cnf(t160,plain,
leq(zero,X1) = true,
inference(orient,[status(thm)],[t18841]) ).
cnf(t19015,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(t19016,plain,
multiplication(antidomain(X1),X2) = multiplication(antidomain(X1),addition(X1,X2)),
inference(step,[status(thm)],[t19015,t31]) ).
cnf(t2352,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t19016]) ).
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(t18832,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)],[t18832]) ).
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(t18836,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)],[t18836]) ).
cnf(t18848,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)],[t18848]) ).
cnf(t2356,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),one),
inference(cp,[status(thm)],[t2352,t206]) ).
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]) ).
cnf(t19017,plain,
multiplication(domain(antidomain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),one),
inference(step,[status(thm)],[t2356,t169]) ).
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]) ).
cnf(t60,plain,
multiplication(addition(X1,antidomain(X2)),X2) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t49,t57]) ).
cnf(t18886,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)],[t18886]) ).
cnf(t541,plain,
multiplication(domain(X1),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t540,t206]) ).
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(t18887,plain,
multiplication(domain(X1),X1) = X1,
inference(step,[status(thm)],[t541,t28]) ).
cnf(t556,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t18887]) ).
cnf(t19018,plain,
antidomain(X1) = multiplication(antidomain(domain(X1)),one),
inference(step,[status(thm)],[t19017,t556]) ).
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(t19019,plain,
antidomain(X1) = antidomain(domain(X1)),
inference(step,[status(thm)],[t19018,t27]) ).
cnf(t19020,plain,
antidomain(X1) = domain(antidomain(X1)),
inference(step,[status(thm)],[t19019,t169]) ).
cnf(t2370,plain,
domain(antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t19020]) ).
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(t18840,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)],[t18840]) ).
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]) ).
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(t18849,plain,
one = domain(one),
inference(step,[status(thm)],[t210,t30]) ).
cnf(t214,plain,
domain(one) = one,
inference(orient,[status(thm)],[t18849]) ).
cnf(t18850,plain,
antidomain(zero) = one,
inference(step,[status(thm)],[t155,t214]) ).
cnf(t215,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t18850]) ).
cnf(t19379,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)],[t19379]) ).
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(t19380,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = addition(one,antidomain(multiplication(X1,domain(coantidomain(X1))))),
inference(step,[status(thm)],[t18411,t31]) ).
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(t18858,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)],[t18858]) ).
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(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(t18859,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t257,t31]) ).
cnf(t18860,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t18859,t66]) ).
cnf(t263,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t18860]) ).
cnf(t19381,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = one,
inference(step,[status(thm)],[t19380,t263]) ).
cnf(t18414,plain,
antidomain(multiplication(X1,domain(coantidomain(X1)))) = one,
inference(orient,[status(thm)],[t19381]) ).
cnf(t18426,plain,
zero = multiplication(one,multiplication(X1,domain(coantidomain(X1)))),
inference(cp,[status(thm)],[t57,t18414]) ).
cnf(t19382,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)],[t19382]) ).
cnf(t18455,plain,
multiplication(X1,addition(domain(coantidomain(X1)),X2)) = addition(zero,multiplication(X1,X2)),
inference(cp,[status(thm)],[t36,t18448]) ).
cnf(t19389,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)],[t19389]) ).
cnf(t18687,plain,
multiplication(X1,antidomain(coantidomain(X1))) = multiplication(X1,one),
inference(cp,[status(thm)],[t18683,t206]) ).
cnf(t19390,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)],[t19390]) ).
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(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(t18983,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)],[t18983]) ).
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]) ).
cnf(t18831,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)],[t18831]) ).
cnf(t18833,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)],[t18833]) ).
cnf(t18842,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)],[t18842]) ).
cnf(t2049,plain,
multiplication(coantidomain(X1),coantidomain(codomain(X1))) = multiplication(one,coantidomain(codomain(X1))),
inference(cp,[status(thm)],[t2045,t182]) ).
cnf(t18984,plain,
multiplication(coantidomain(X1),codomain(coantidomain(X1))) = multiplication(one,coantidomain(codomain(X1))),
inference(step,[status(thm)],[t2049,t167]) ).
cnf(t44,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t36,t40]) ).
cnf(t18883,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)],[t18883]) ).
cnf(t502,plain,
multiplication(X1,codomain(X1)) = multiplication(X1,one),
inference(cp,[status(thm)],[t500,t182]) ).
cnf(t18884,plain,
multiplication(X1,codomain(X1)) = X1,
inference(step,[status(thm)],[t502,t27]) ).
cnf(t517,plain,
multiplication(X1,codomain(X1)) = X1,
inference(orient,[status(thm)],[t18884]) ).
cnf(t18985,plain,
coantidomain(X1) = multiplication(one,coantidomain(codomain(X1))),
inference(step,[status(thm)],[t18984,t517]) ).
cnf(t18986,plain,
coantidomain(X1) = coantidomain(codomain(X1)),
inference(step,[status(thm)],[t18985,t28]) ).
cnf(t18987,plain,
coantidomain(X1) = codomain(coantidomain(X1)),
inference(step,[status(thm)],[t18986,t167]) ).
cnf(t2069,plain,
codomain(coantidomain(X1)) = coantidomain(X1),
inference(orient,[status(thm)],[t18987]) ).
cnf(t18988,plain,
coantidomain(codomain(X1)) = coantidomain(X1),
inference(step,[status(thm)],[t167,t2069]) ).
cnf(t2070,plain,
coantidomain(codomain(X1)) = coantidomain(X1),
inference(orient,[status(thm)],[t18988]) ).
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(t19166,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)],[t19166]) ).
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(t18982,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)],[t18982]) ).
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(t18861,plain,
one = addition(coantidomain(X1),one),
inference(step,[status(thm)],[t261,t31]) ).
cnf(t18862,plain,
one = addition(one,coantidomain(X1)),
inference(step,[status(thm)],[t18861,t66]) ).
cnf(t267,plain,
addition(one,coantidomain(X1)) = one,
inference(orient,[status(thm)],[t18862]) ).
cnf(t2026,plain,
addition(coantidomain(X1),domain(coantidomain(X1))) = multiplication(domain(coantidomain(X1)),one),
inference(cp,[status(thm)],[t2014,t267]) ).
cnf(t18999,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)],[t18999]) ).
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(t18854,plain,
one = addition(domain(X1),one),
inference(step,[status(thm)],[t221,t206]) ).
cnf(t18855,plain,
one = addition(one,domain(X1)),
inference(step,[status(thm)],[t18854,t66]) ).
cnf(t227,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t18855]) ).
cnf(t19040,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)],[t19040]) ).
cnf(t7978,plain,
multiplication(codomain(X1),antidomain(coantidomain(X1))) = multiplication(one,antidomain(coantidomain(X1))),
inference(cp,[status(thm)],[t7974,t2919]) ).
cnf(t19168,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)],[t19168]) ).
cnf(t19391,plain,
codomain(X1) = antidomain(coantidomain(X1)),
inference(step,[status(thm)],[t18731,t8029]) ).
cnf(t18756,plain,
antidomain(coantidomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t19391]) ).
cnf(t18759,plain,
antidomain(coantidomain(X1)) = domain(codomain(X1)),
inference(cp,[status(thm)],[t2370,t18756]) ).
cnf(t19399,plain,
codomain(X1) = domain(codomain(X1)),
inference(step,[status(thm)],[t18759,t18756]) ).
cnf(t18820,plain,
domain(codomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t19399]) ).
fof(f20,conjecture,
! [X0] : domain(codomain(X0)) = codomain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0] : domain(codomain(X0)) = codomain(X0),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0] : domain(codomain(X0)) != codomain(X0),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
domain(codomain(sk0)) != codomain(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f20_nnf]) ).
cnf(c21,plain,
domain(codomain(sk0)) != codomain(sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
domain(codomain(sk0)) != codomain(sk0),
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
codomain(sk0) != codomain(sk0),
inference(rw,[status(thm)],[goal_0,t18820]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE091+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 18:55:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.79/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.79/2.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------