%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE113+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 3.99s 1.09s
% Output : Proof 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 74 ( 74 unt; 0 def)
% Number of atoms : 74 ( 73 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 6 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(t21,plain,
domain(multiplication(X1,domain(X2))) = forward_diamond(X1,X2),
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t172,plain,
domain(multiplication(X1,domain(X2))) = forward_diamond(X1,X2),
inference(orient,[status(thm)],[t21]) ).
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(t9,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t91,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9]) ).
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(t13,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t55,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t13]) ).
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(t5,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t33,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t56,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t55,t33]) ).
cnf(t196,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t56]) ).
cnf(t198,plain,
domain(one) = antidomain(zero),
inference(cp,[status(thm)],[t91,t196]) ).
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(t16,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(t14,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t100,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t230,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t16,t100]) ).
cnf(t231,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t230,t91]) ).
cnf(t232,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t231,t100]) ).
cnf(t114,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t232]) ).
cnf(t197,plain,
one = addition(domain(one),zero),
inference(cp,[status(thm)],[t114,t196]) ).
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(t36,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t239,plain,
one = domain(one),
inference(step,[status(thm)],[t197,t36]) ).
cnf(t200,plain,
domain(one) = one,
inference(orient,[status(thm)],[t239]) ).
cnf(t241,plain,
one = antidomain(zero),
inference(step,[status(thm)],[t198,t200]) ).
cnf(t209,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t241]) ).
cnf(t211,plain,
domain(zero) = antidomain(one),
inference(cp,[status(thm)],[t91,t209]) ).
cnf(t242,plain,
domain(zero) = zero,
inference(step,[status(thm)],[t211,t196]) ).
cnf(t213,plain,
domain(zero) = zero,
inference(orient,[status(thm)],[t242]) ).
cnf(t217,plain,
forward_diamond(X1,zero) = domain(multiplication(X1,zero)),
inference(cp,[status(thm)],[t172,t213]) ).
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(t6,plain,
multiplication(X1,zero) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t52,plain,
multiplication(X1,zero) = zero,
inference(orient,[status(thm)],[t6]) ).
cnf(t247,plain,
forward_diamond(X1,zero) = domain(zero),
inference(step,[status(thm)],[t217,t52]) ).
cnf(t248,plain,
forward_diamond(X1,zero) = zero,
inference(step,[status(thm)],[t247,t213]) ).
cnf(t227,plain,
forward_diamond(X1,zero) = zero,
inference(orient,[status(thm)],[t248]) ).
fof(f26,conjecture,
! [X0] : forward_diamond(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f26_neg,negated_conjecture,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [X0] : forward_diamond(X0,zero) != zero,
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
forward_diamond(sk0,zero) != zero,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f26_nnf]) ).
cnf(c27,plain,
forward_diamond(sk0,zero) != zero,
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
forward_diamond(sk0,zero) != zero,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t227]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.56 % Computer : n017.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Wed Sep 23 18:54:15 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.99/1.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.99/1.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------