%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE040+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 01:51:27 PM UTC 2026
% Result : Theorem 23.99s 3.57s
% Output : Proof 23.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 132 ( 123 unt; 0 def)
% Number of atoms : 145 ( 125 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 9 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 229 ( 28 sgn 62 !; 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(t13,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t28,plain,
ifeq(leq(X1,X2),true,addition(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t13]) ).
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(t9,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t31,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t33,plain,
X1 = ifeq(leq(X2,X1),true,addition(X1,X2),X1),
inference(cp,[status(thm)],[t28,t31]) ).
cnf(t322,plain,
ifeq(leq(X1,X2),true,addition(X2,X1),X2) = X2,
inference(orient,[status(thm)],[t33]) ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
fof(f14_nnf,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t22,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t92,plain,
ifeq(leq(addition(multiplication(X1,X2),X3),X2),true,leq(multiplication(star(X1),X3),X2),true) = true,
inference(orient,[status(thm)],[t22]) ).
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(t20,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)],[t20]) ).
cnf(t93,plain,
true = ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true),
inference(cp,[status(thm)],[t92,t49]) ).
cnf(t20391,plain,
ifeq(leq(multiplication(addition(X1,X2),X3),X3),true,leq(multiplication(star(X1),multiplication(X2,X3)),X3),true) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
fof(f12,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f12_nnf,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi13,axiom,
leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t17,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
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(t11,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t34,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t20560,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t17,t34]) ).
cnf(t20561,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t20560,t31]) ).
cnf(t41,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t20561]) ).
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(t26,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t51,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t26]) ).
cnf(t179,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t51]) ).
cnf(t20572,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(step,[status(thm)],[t41,t179]) ).
cnf(t191,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[t20572]) ).
cnf(t473,plain,
addition(one,multiplication(addition(one,X1),star(X1))) = star(X1),
inference(orient,[status(thm)],[t191]) ).
cnf(t480,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(leq(one,multiplication(addition(one,X1),star(X1))),true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(cp,[status(thm)],[t28,t473]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t12,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t82,plain,
ifeq(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t12]) ).
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(t23,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t37,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t34,t23]) ).
cnf(t135,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t142,plain,
true = ifeq(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t82,t135]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t27,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t20571,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t142,t27]) ).
cnf(t150,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t20571]) ).
cnf(t154,plain,
true = leq(X1,addition(X2,X1)),
inference(cp,[status(thm)],[t150,t31]) ).
cnf(t157,plain,
leq(X1,addition(X2,X1)) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t162,plain,
true = leq(X1,addition(X2,addition(X3,X1))),
inference(cp,[status(thm)],[t157,t34]) ).
cnf(t229,plain,
leq(X1,addition(X2,addition(X3,X1))) = true,
inference(orient,[status(thm)],[t162]) ).
cnf(t231,plain,
true = leq(X1,addition(addition(X2,X1),X3)),
inference(cp,[status(thm)],[t229,t31]) ).
cnf(t20574,plain,
true = leq(X1,addition(X2,addition(X1,X3))),
inference(step,[status(thm)],[t231,t34]) ).
cnf(t277,plain,
leq(X1,addition(X2,addition(X1,X3))) = true,
inference(orient,[status(thm)],[t20574]) ).
cnf(t137,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t135,t41]) ).
cnf(t20569,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t137,t41]) ).
cnf(t145,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t20569]) ).
cnf(t283,plain,
true = leq(one,addition(X1,star(X2))),
inference(cp,[status(thm)],[t277,t145]) ).
cnf(t289,plain,
leq(one,addition(X1,star(X2))) = true,
inference(orient,[status(thm)],[t283]) ).
cnf(t291,plain,
true = leq(one,addition(star(X1),X2)),
inference(cp,[status(thm)],[t289,t31]) ).
cnf(t294,plain,
leq(one,addition(star(X1),X2)) = true,
inference(orient,[status(thm)],[t291]) ).
cnf(t295,plain,
true = leq(one,multiplication(addition(one,X1),star(X2))),
inference(cp,[status(thm)],[t294,t179]) ).
cnf(t382,plain,
leq(one,multiplication(addition(one,X1),star(X2))) = true,
inference(orient,[status(thm)],[t295]) ).
cnf(t20581,plain,
multiplication(addition(one,X1),star(X1)) = ifeq(true,true,star(X1),multiplication(addition(one,X1),star(X1))),
inference(step,[status(thm)],[t480,t382]) ).
cnf(t20582,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(step,[status(thm)],[t20581,t27]) ).
cnf(t494,plain,
multiplication(addition(one,X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t20582]) ).
cnf(t500,plain,
star(X1) = multiplication(addition(X1,one),star(X1)),
inference(cp,[status(thm)],[t494,t31]) ).
cnf(t581,plain,
multiplication(addition(X1,one),star(X1)) = star(X1),
inference(orient,[status(thm)],[t500]) ).
cnf(t20399,plain,
true = ifeq(leq(star(X1),star(X1)),true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(cp,[status(thm)],[t20391,t581]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(hi3,axiom,
addition(X0,X0) = X0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t3,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi3]) ).
cnf(t72,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t20665,plain,
true = ifeq(true,true,leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),true),
inference(step,[status(thm)],[t20399,t72]) ).
cnf(t20666,plain,
true = leq(multiplication(star(X1),multiplication(one,star(X1))),star(X1)),
inference(step,[status(thm)],[t20665,t27]) ).
cnf(t20667,plain,
true = leq(multiplication(star(X1),star(X1)),star(X1)),
inference(step,[status(thm)],[t20666,t26]) ).
cnf(t20514,plain,
leq(multiplication(star(X1),star(X1)),star(X1)) = true,
inference(orient,[status(thm)],[t20667]) ).
cnf(t20517,plain,
star(X1) = ifeq(true,true,addition(star(X1),multiplication(star(X1),star(X1))),star(X1)),
inference(cp,[status(thm)],[t322,t20514]) ).
cnf(t20668,plain,
star(X1) = addition(star(X1),multiplication(star(X1),star(X1))),
inference(step,[status(thm)],[t20517,t27]) ).
cnf(t20669,plain,
star(X1) = multiplication(addition(one,star(X1)),star(X1)),
inference(step,[status(thm)],[t20668,t179]) ).
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(t19,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)],[t19]) ).
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(t25,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t57,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t55,t25]) ).
cnf(t192,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t57]) ).
cnf(t193,plain,
multiplication(X1,addition(one,X1)) = multiplication(addition(one,X1),X1),
inference(cp,[status(thm)],[t192,t179]) ).
cnf(t205,plain,
multiplication(addition(one,X1),X1) = multiplication(X1,addition(one,X1)),
inference(orient,[status(thm)],[t193]) ).
cnf(t20670,plain,
star(X1) = multiplication(star(X1),addition(one,star(X1))),
inference(step,[status(thm)],[t20669,t205]) ).
cnf(t20671,plain,
star(X1) = multiplication(star(X1),star(X1)),
inference(step,[status(thm)],[t20670,t145]) ).
cnf(t20521,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(orient,[status(thm)],[t20671]) ).
fof(f16,conjecture,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16_neg,negated_conjecture,
~ ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
? [X0] : multiplication(star(X0),star(X0)) != star(X0),
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
multiplication(star(sk0),star(sk0)) != star(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f16_nnf]) ).
cnf(c17,plain,
multiplication(star(sk0),star(sk0)) != star(sk0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(star(sk0),star(sk0)) != star(sk0),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
star(sk0) != star(sk0),
inference(rw,[status(thm)],[goal_0,t20521]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Wed Sep 23 18:47:04 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.99/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.99/3.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------