%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE078+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 : n016.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 01:51:33 PM UTC 2026
% Result : Theorem 8.98s 1.62s
% Output : Proof 8.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 17
% Syntax : Number of formulae : 236 ( 227 unt; 0 def)
% Number of atoms : 253 ( 245 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 6 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 333 ( 19 sgn 78 !; 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(t25,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)],[t25]) ).
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(t24,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t55,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t24]) ).
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(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t28,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t57,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t55,t28]) ).
cnf(t358,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t57]) ).
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t19,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t44,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t19]) ).
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(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t29,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t51,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t29]) ).
cnf(t328,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t51]) ).
cnf(t6611,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t44,t328]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
addition(domain(X1),one) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
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(t12,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t34,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t6586,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t34]) ).
cnf(t65,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t6586]) ).
cnf(t6612,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t6611,t65]) ).
cnf(t6613,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t6612,t29]) ).
cnf(t339,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t6613]) ).
cnf(t340,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t339]) ).
cnf(t362,plain,
multiplication(domain(X1),addition(one,X1)) = addition(domain(X1),X1),
inference(cp,[status(thm)],[t358,t340]) ).
cnf(t6628,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(step,[status(thm)],[t362,t34]) ).
cnf(t682,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t6628]) ).
cnf(t702,plain,
addition(X1,domain(X1)) = multiplication(domain(X1),addition(X1,one)),
inference(cp,[status(thm)],[t682,t34]) ).
cnf(t728,plain,
multiplication(domain(X1),addition(X1,one)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t702]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t18,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t85,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t18]) ).
fof(f16,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain5) ).
fof(f16_nnf,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t17,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t61,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t17]) ).
cnf(t87,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t85,t29]) ).
cnf(t6588,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t87,t29]) ).
cnf(t119,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t6588]) ).
cnf(t122,plain,
domain(addition(domain(X1),X2)) = addition(domain(X1),domain(X2)),
inference(cp,[status(thm)],[t61,t119]) ).
cnf(t6602,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(step,[status(thm)],[t122,t61]) ).
cnf(t227,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(orient,[status(thm)],[t6602]) ).
fof(f17,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> domain(antidomain(X0)) = antidomain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> domain(antidomain(X0)) = antidomain(X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0] :
( domain(antidomain(X0)) != antidomain(X0)
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
! [X1] :
( domain(antidomain(sk0)) != antidomain(sk0)
& multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c18,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t13,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t68,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t13]) ).
cnf(t229,plain,
domain(addition(X1,antidomain(X1))) = domain(one),
inference(cp,[status(thm)],[t227,t68]) ).
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(t22,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t31,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(hi13,axiom,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t16,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi13]) ).
cnf(t98,plain,
leq(X1,multiplication(domain(X1),X1)) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t99,plain,
true = leq(one,domain(one)),
inference(cp,[status(thm)],[t98,t28]) ).
cnf(t127,plain,
leq(one,domain(one)) = true,
inference(orient,[status(thm)],[t99]) ).
cnf(t128,plain,
domain(one) = ifeq(true,true,addition(one,domain(one)),domain(one)),
inference(cp,[status(thm)],[t31,t127]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t6590,plain,
domain(one) = addition(one,domain(one)),
inference(step,[status(thm)],[t128,t30]) ).
cnf(t6591,plain,
domain(one) = one,
inference(step,[status(thm)],[t6590,t65]) ).
cnf(t130,plain,
domain(one) = one,
inference(orient,[status(thm)],[t6591]) ).
cnf(t6603,plain,
domain(addition(X1,antidomain(X1))) = one,
inference(step,[status(thm)],[t229,t130]) ).
cnf(t244,plain,
domain(addition(X1,antidomain(X1))) = one,
inference(orient,[status(thm)],[t6603]) ).
cnf(t251,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(multiplication(X1,one)),
inference(cp,[status(thm)],[t85,t244]) ).
cnf(t6630,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(step,[status(thm)],[t251,t28]) ).
cnf(t743,plain,
domain(multiplication(X1,addition(X2,antidomain(X2)))) = domain(X1),
inference(orient,[status(thm)],[t6630]) ).
cnf(c19,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t15,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t77,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(orient,[status(thm)],[t15]) ).
cnf(t80,plain,
multiplication(domain(X1),addition(X2,antidomain(X1))) = addition(multiplication(domain(X1),X2),zero),
inference(cp,[status(thm)],[t55,t77]) ).
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(t2,plain,
addition(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t27,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t6667,plain,
multiplication(domain(X1),addition(X2,antidomain(X1))) = multiplication(domain(X1),X2),
inference(step,[status(thm)],[t80,t27]) ).
cnf(t2238,plain,
multiplication(domain(X1),addition(X2,antidomain(X1))) = multiplication(domain(X1),X2),
inference(orient,[status(thm)],[t6667]) ).
cnf(t2249,plain,
multiplication(domain(X1),X2) = multiplication(domain(X1),addition(antidomain(X1),X2)),
inference(cp,[status(thm)],[t2238,t34]) ).
cnf(t2477,plain,
multiplication(domain(X1),addition(antidomain(X1),X2)) = multiplication(domain(X1),X2),
inference(orient,[status(thm)],[t2249]) ).
cnf(t2498,plain,
domain(domain(X1)) = domain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(cp,[status(thm)],[t743,t2477]) ).
cnf(t6676,plain,
domain(X1) = domain(multiplication(domain(X1),antidomain(antidomain(X1)))),
inference(step,[status(thm)],[t2498,t119]) ).
cnf(t2499,plain,
domain(multiplication(domain(X1),antidomain(antidomain(X1)))) = domain(X1),
inference(orient,[status(thm)],[t6676]) ).
cnf(t82,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = addition(multiplication(X1,antidomain(X2)),zero),
inference(cp,[status(thm)],[t49,t77]) ).
cnf(t6668,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(step,[status(thm)],[t82,t27]) ).
cnf(t2257,plain,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(orient,[status(thm)],[t6668]) ).
cnf(t2259,plain,
multiplication(domain(X1),antidomain(X2)) = multiplication(domain(addition(X1,X2)),antidomain(X2)),
inference(cp,[status(thm)],[t2257,t61]) ).
cnf(t3658,plain,
multiplication(domain(addition(X1,X2)),antidomain(X2)) = multiplication(domain(X1),antidomain(X2)),
inference(orient,[status(thm)],[t2259]) ).
cnf(t3668,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = multiplication(one,antidomain(antidomain(X1))),
inference(cp,[status(thm)],[t3658,t244]) ).
cnf(t6698,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t3668,t29]) ).
cnf(t3702,plain,
multiplication(domain(X1),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(orient,[status(thm)],[t6698]) ).
cnf(t6699,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(step,[status(thm)],[t2499,t3702]) ).
cnf(t3733,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(rw,[status(thm)],[t6699]) ).
cnf(t3734,plain,
domain(antidomain(antidomain(X1))) = domain(X1),
inference(orient,[status(thm)],[t3733]) ).
cnf(t3770,plain,
domain(multiplication(X1,antidomain(antidomain(X2)))) = domain(multiplication(X1,domain(X2))),
inference(cp,[status(thm)],[t85,t3734]) ).
cnf(t6709,plain,
domain(multiplication(X1,antidomain(antidomain(X2)))) = domain(multiplication(X1,X2)),
inference(step,[status(thm)],[t3770,t85]) ).
cnf(t4452,plain,
domain(multiplication(X1,antidomain(antidomain(X2)))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t6709]) ).
cnf(t4465,plain,
domain(multiplication(domain(antidomain(X1)),X1)) = domain(zero),
inference(cp,[status(thm)],[t4452,t77]) ).
fof(f15,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
fof(f15_nnf,plain,
domain(zero) = zero,
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t0,plain,
domain(zero) = zero,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t94,plain,
domain(zero) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t6714,plain,
domain(multiplication(domain(antidomain(X1)),X1)) = zero,
inference(step,[status(thm)],[t4465,t94]) ).
cnf(t4592,plain,
domain(multiplication(domain(antidomain(X1)),X1)) = zero,
inference(orient,[status(thm)],[t6714]) ).
cnf(t4594,plain,
addition(multiplication(domain(antidomain(X1)),X1),domain(multiplication(domain(antidomain(X1)),X1))) = multiplication(zero,addition(multiplication(domain(antidomain(X1)),X1),one)),
inference(cp,[status(thm)],[t728,t4592]) ).
cnf(t6715,plain,
addition(multiplication(domain(antidomain(X1)),X1),zero) = multiplication(zero,addition(multiplication(domain(antidomain(X1)),X1),one)),
inference(step,[status(thm)],[t4594,t4592]) ).
cnf(t6716,plain,
multiplication(domain(antidomain(X1)),X1) = multiplication(zero,addition(multiplication(domain(antidomain(X1)),X1),one)),
inference(step,[status(thm)],[t6715,t27]) ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f10_nnf,plain,
! [A] : multiplication(zero,A) = zero,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : multiplication(zero,A) = zero,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t9,plain,
multiplication(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t83,plain,
multiplication(zero,X1) = zero,
inference(orient,[status(thm)],[t9]) ).
cnf(t6717,plain,
multiplication(domain(antidomain(X1)),X1) = zero,
inference(step,[status(thm)],[t6716,t83]) ).
cnf(t4624,plain,
multiplication(domain(antidomain(X1)),X1) = zero,
inference(orient,[status(thm)],[t6717]) ).
cnf(t4629,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = addition(zero,multiplication(X2,X1)),
inference(cp,[status(thm)],[t49,t4624]) ).
cnf(t35,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t34,t27]) ).
cnf(t114,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t35]) ).
cnf(t6751,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(step,[status(thm)],[t4629,t114]) ).
cnf(t6466,plain,
multiplication(addition(domain(antidomain(X1)),X2),X1) = multiplication(X2,X1),
inference(orient,[status(thm)],[t6751]) ).
cnf(t6470,plain,
multiplication(antidomain(antidomain(X1)),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t6466,t68]) ).
cnf(t6752,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(step,[status(thm)],[t6470,t29]) ).
cnf(t6505,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(orient,[status(thm)],[t6752]) ).
cnf(t21,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t104,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t21]) ).
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(t20,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t37,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t20]) ).
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(t1,plain,
addition(X1,X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t40,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t37,t26]) ).
cnf(t155,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t40]) ).
cnf(t161,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t104,t155]) ).
cnf(t6596,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t161,t30]) ).
cnf(t162,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t6596]) ).
cnf(t167,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t162,t34]) ).
cnf(t168,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t167]) ).
cnf(t170,plain,
true = leq(antidomain(X1),one),
inference(cp,[status(thm)],[t168,t68]) ).
cnf(t176,plain,
leq(antidomain(X1),one) = true,
inference(orient,[status(thm)],[t170]) ).
cnf(t177,plain,
one = ifeq(true,true,addition(antidomain(X1),one),one),
inference(cp,[status(thm)],[t31,t176]) ).
cnf(t6597,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t177,t30]) ).
cnf(t6598,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t6597,t34]) ).
cnf(t179,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t6598]) ).
cnf(t700,plain,
addition(antidomain(X1),domain(antidomain(X1))) = multiplication(domain(antidomain(X1)),one),
inference(cp,[status(thm)],[t682,t179]) ).
cnf(t6629,plain,
addition(antidomain(X1),domain(antidomain(X1))) = domain(antidomain(X1)),
inference(step,[status(thm)],[t700,t28]) ).
cnf(t710,plain,
addition(antidomain(X1),domain(antidomain(X1))) = domain(antidomain(X1)),
inference(orient,[status(thm)],[t6629]) ).
cnf(t2258,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = multiplication(domain(antidomain(X1)),antidomain(antidomain(X1))),
inference(cp,[status(thm)],[t2257,t710]) ).
cnf(t6669,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(step,[status(thm)],[t2258,t77]) ).
cnf(t2279,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(orient,[status(thm)],[t6669]) ).
cnf(t4456,plain,
domain(multiplication(antidomain(X1),X1)) = domain(zero),
inference(cp,[status(thm)],[t4452,t2279]) ).
cnf(t6710,plain,
domain(multiplication(antidomain(X1),X1)) = zero,
inference(step,[status(thm)],[t4456,t94]) ).
cnf(t4550,plain,
domain(multiplication(antidomain(X1),X1)) = zero,
inference(orient,[status(thm)],[t6710]) ).
cnf(t4553,plain,
addition(multiplication(antidomain(X1),X1),domain(multiplication(antidomain(X1),X1))) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(cp,[status(thm)],[t728,t4550]) ).
cnf(t6711,plain,
addition(multiplication(antidomain(X1),X1),zero) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(step,[status(thm)],[t4553,t4550]) ).
cnf(t6712,plain,
multiplication(antidomain(X1),X1) = multiplication(zero,addition(multiplication(antidomain(X1),X1),one)),
inference(step,[status(thm)],[t6711,t27]) ).
cnf(t6713,plain,
multiplication(antidomain(X1),X1) = zero,
inference(step,[status(thm)],[t6712,t83]) ).
cnf(t4583,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t6713]) ).
cnf(t4586,plain,
multiplication(antidomain(X1),addition(X1,X2)) = addition(zero,multiplication(antidomain(X1),X2)),
inference(cp,[status(thm)],[t55,t4583]) ).
cnf(t6730,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(step,[status(thm)],[t4586,t114]) ).
cnf(t5356,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t6730]) ).
cnf(t5365,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = multiplication(antidomain(domain(X1)),one),
inference(cp,[status(thm)],[t5356,t68]) ).
cnf(t2261,plain,
multiplication(X1,antidomain(X2)) = multiplication(addition(domain(X2),X1),antidomain(X2)),
inference(cp,[status(thm)],[t2257,t34]) ).
cnf(t2554,plain,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(orient,[status(thm)],[t2261]) ).
cnf(t121,plain,
one = addition(domain(X1),antidomain(domain(X1))),
inference(cp,[status(thm)],[t68,t119]) ).
cnf(t198,plain,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(orient,[status(thm)],[t121]) ).
cnf(t2559,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = multiplication(one,antidomain(X1)),
inference(cp,[status(thm)],[t2554,t198]) ).
cnf(t6678,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(step,[status(thm)],[t2559,t29]) ).
cnf(t2588,plain,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t6678]) ).
cnf(t6731,plain,
antidomain(X1) = multiplication(antidomain(domain(X1)),one),
inference(step,[status(thm)],[t5365,t2588]) ).
cnf(t6732,plain,
antidomain(X1) = antidomain(domain(X1)),
inference(step,[status(thm)],[t6731,t28]) ).
cnf(t5379,plain,
antidomain(domain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t6732]) ).
cnf(t6516,plain,
domain(X1) = multiplication(antidomain(antidomain(X1)),domain(X1)),
inference(cp,[status(thm)],[t6505,t5379]) ).
cnf(t4587,plain,
multiplication(antidomain(X1),addition(X2,X1)) = addition(multiplication(antidomain(X1),X2),zero),
inference(cp,[status(thm)],[t55,t4583]) ).
cnf(t6741,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(step,[status(thm)],[t4587,t27]) ).
cnf(t5989,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(orient,[status(thm)],[t6741]) ).
cnf(t6012,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = multiplication(antidomain(antidomain(X1)),one),
inference(cp,[status(thm)],[t5989,t68]) ).
cnf(t6742,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t6012,t28]) ).
cnf(t6029,plain,
multiplication(antidomain(antidomain(X1)),domain(X1)) = antidomain(antidomain(X1)),
inference(orient,[status(thm)],[t6742]) ).
cnf(t6753,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(step,[status(thm)],[t6516,t6029]) ).
cnf(t6527,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t6753]) ).
cnf(t6528,plain,
domain(antidomain(X1)) = antidomain(domain(X1)),
inference(cp,[status(thm)],[t6527,t6527]) ).
cnf(t6755,plain,
domain(antidomain(X1)) = antidomain(X1),
inference(step,[status(thm)],[t6528,t5379]) ).
cnf(t6558,plain,
domain(antidomain(X1)) = antidomain(X1),
inference(orient,[status(thm)],[t6755]) ).
cnf(c20,plain,
domain(antidomain(sk0)) != antidomain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
domain(antidomain(sk0)) != antidomain(sk0),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
antidomain(sk0) != antidomain(sk0),
inference(rw,[status(thm)],[goal_0,t6558]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE078+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 18:56:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.98/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.98/1.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------