%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 01:51:38 PM UTC 2026
% Result : Theorem 8.12s 1.69s
% Output : Proof 8.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 96 ( 96 unt; 0 def)
% Number of atoms : 96 ( 95 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 9 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_box) ).
fof(f24_nnf,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X0,X1] : forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c25,plain,
forward_box(X0,X1) = c(forward_diamond(X0,c(X1))),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t17,plain,
c(forward_diamond(X1,c(X2))) = forward_box(X1,X2),
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t182,plain,
c(forward_diamond(X1,c(X2))) = forward_box(X1,X2),
inference(orient,[status(thm)],[t17]) ).
fof(f20,axiom,
! [X0] : c(X0) = antidomain(domain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f20_nnf,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c21,plain,
c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t8,plain,
antidomain(domain(X1)) = c(X1),
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t94,plain,
antidomain(domain(X1)) = c(X1),
inference(orient,[status(thm)],[t8]) ).
fof(f14,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/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(t14,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f0,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/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(t98,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t298,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t14,t98]) ).
fof(f15,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/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(t7,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t89,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t299,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t298,t89]) ).
cnf(t300,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t299,t98]) ).
cnf(t112,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t300]) ).
fof(f12,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/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(t11,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t53,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t11]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/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(t3,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t31,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t54,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t53,t31]) ).
cnf(t194,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t54]) ).
cnf(t195,plain,
one = addition(domain(one),zero),
inference(cp,[status(thm)],[t112,t194]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/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(t34,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t307,plain,
one = domain(one),
inference(step,[status(thm)],[t195,t34]) ).
cnf(t198,plain,
domain(one) = one,
inference(orient,[status(thm)],[t307]) ).
cnf(t199,plain,
c(one) = antidomain(one),
inference(cp,[status(thm)],[t94,t198]) ).
cnf(t308,plain,
c(one) = zero,
inference(step,[status(thm)],[t199,t194]) ).
cnf(t202,plain,
c(one) = zero,
inference(orient,[status(thm)],[t308]) ).
cnf(t203,plain,
forward_box(X1,one) = c(forward_diamond(X1,zero)),
inference(cp,[status(thm)],[t182,t202]) ).
fof(f22,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',forward_diamond) ).
fof(f22_nnf,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c23,plain,
forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t19,plain,
domain(multiplication(X1,domain(X2))) = forward_diamond(X1,X2),
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t170,plain,
domain(multiplication(X1,domain(X2))) = forward_diamond(X1,X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t196,plain,
domain(one) = antidomain(zero),
inference(cp,[status(thm)],[t89,t194]) ).
cnf(t309,plain,
one = antidomain(zero),
inference(step,[status(thm)],[t196,t198]) ).
cnf(t207,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t309]) ).
cnf(t209,plain,
domain(zero) = antidomain(one),
inference(cp,[status(thm)],[t89,t207]) ).
cnf(t310,plain,
domain(zero) = zero,
inference(step,[status(thm)],[t209,t194]) ).
cnf(t211,plain,
domain(zero) = zero,
inference(orient,[status(thm)],[t310]) ).
cnf(t215,plain,
forward_diamond(X1,zero) = domain(multiplication(X1,zero)),
inference(cp,[status(thm)],[t170,t211]) ).
fof(f9,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
fof(f9_nnf,plain,
! [A] : multiplication(A,zero) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : multiplication(A,zero) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t4,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t50,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t315,plain,
forward_diamond(X1,zero) = domain(zero),
inference(step,[status(thm)],[t215,t50]) ).
cnf(t316,plain,
forward_diamond(X1,zero) = zero,
inference(step,[status(thm)],[t315,t211]) ).
cnf(t225,plain,
forward_diamond(X1,zero) = zero,
inference(orient,[status(thm)],[t316]) ).
cnf(t329,plain,
forward_box(X1,one) = c(zero),
inference(step,[status(thm)],[t203,t225]) ).
cnf(t213,plain,
c(zero) = antidomain(zero),
inference(cp,[status(thm)],[t94,t211]) ).
cnf(t311,plain,
c(zero) = one,
inference(step,[status(thm)],[t213,t207]) ).
cnf(t216,plain,
c(zero) = one,
inference(orient,[status(thm)],[t311]) ).
cnf(t330,plain,
forward_box(X1,one) = one,
inference(step,[status(thm)],[t329,t216]) ).
cnf(t295,plain,
forward_box(X1,one) = one,
inference(orient,[status(thm)],[t330]) ).
fof(f26,conjecture,
! [X0] : forward_box(X0,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f26_neg,negated_conjecture,
~ ! [X0] : forward_box(X0,one) = one,
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [X0] : forward_box(X0,one) != one,
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
forward_box(sk0,one) != one,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f26_nnf]) ).
cnf(c27,plain,
forward_box(sk0,one) != one,
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
forward_box(sk0,one) != one,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
one != one,
inference(rw,[status(thm)],[goal_0,t295]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE114+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Wed Sep 23 18:54:32 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.12/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.12/1.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------