%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE119+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 : 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 01:51:39 PM UTC 2026
% Result : Theorem 9.42s 1.73s
% Output : Proof 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 73 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 4 con; 0-2 aty)
% Number of variables : 73 ( 5 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(t98,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
fof(f23,axiom,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
fof(f23_nnf,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X0,X1] : backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c24,plain,
backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t18,plain,
codomain(multiplication(codomain(X1),X2)) = backward_diamond(X2,X1),
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t186,plain,
codomain(multiplication(codomain(X1),X2)) = backward_diamond(X2,X1),
inference(orient,[status(thm)],[t18]) ).
fof(f9,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/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(t187,plain,
backward_diamond(zero,X1) = codomain(zero),
inference(cp,[status(thm)],[t186,t50]) ).
cnf(t230,plain,
backward_diamond(zero,X1) = codomain(zero),
inference(orient,[status(thm)],[t187]) ).
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(t15,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t435,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(step,[status(thm)],[t15,t98]) ).
cnf(t129,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(orient,[status(thm)],[t435]) ).
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(t9,plain,
coantidomain(coantidomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t132,plain,
coantidomain(coantidomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t436,plain,
addition(coantidomain(X1),codomain(X1)) = one,
inference(step,[status(thm)],[t129,t132]) ).
cnf(t135,plain,
addition(coantidomain(X1),codomain(X1)) = one,
inference(rw,[status(thm)],[t436]) ).
cnf(t478,plain,
addition(codomain(X1),coantidomain(X1)) = one,
inference(step,[status(thm)],[t135,t98]) ).
cnf(t414,plain,
addition(codomain(X1),coantidomain(X1)) = one,
inference(orient,[status(thm)],[t478]) ).
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(t10,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t44,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(orient,[status(thm)],[t10]) ).
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(t5,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t46,plain,
zero = coantidomain(one),
inference(cp,[status(thm)],[t44,t32]) ).
cnf(t192,plain,
coantidomain(one) = zero,
inference(orient,[status(thm)],[t46]) ).
cnf(t420,plain,
one = addition(codomain(one),zero),
inference(cp,[status(thm)],[t414,t192]) ).
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(t34,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t479,plain,
one = codomain(one),
inference(step,[status(thm)],[t420,t34]) ).
cnf(t424,plain,
codomain(one) = one,
inference(orient,[status(thm)],[t479]) ).
fof(f26,conjecture,
! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f26_neg,negated_conjecture,
~ ! [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) = domain(X1),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [X0,X1] : addition(backward_diamond(zero,domain(X0)),domain(X1)) != domain(X1),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
addition(backward_diamond(zero,domain(sk0)),domain(sk1)) != domain(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f26_nnf]) ).
cnf(c27,plain,
addition(backward_diamond(zero,domain(sk0)),domain(sk1)) != domain(sk1),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
addition(backward_diamond(zero,domain(sk0)),domain(sk1)) != domain(sk1),
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(g0_0,plain,
addition(domain(sk1),backward_diamond(zero,domain(sk0))) != domain(sk1),
inference(rw,[status(thm)],[goal_0,t98]) ).
cnf(g0_1,plain,
addition(domain(sk1),codomain(zero)) != domain(sk1),
inference(rw,[status(thm)],[g0_0,t230]) ).
cnf(g0_2,plain,
addition(domain(sk1),coantidomain(codomain(one))) != domain(sk1),
inference(rw,[status(thm)],[g0_1]) ).
cnf(g0_3,plain,
addition(domain(sk1),coantidomain(one)) != domain(sk1),
inference(rw,[status(thm)],[g0_2,t424]) ).
cnf(g0_4,plain,
addition(domain(sk1),zero) != domain(sk1),
inference(rw,[status(thm)],[g0_3,t192]) ).
cnf(g0_5,plain,
domain(sk1) != domain(sk1),
inference(rw,[status(thm)],[g0_4,t34]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE119+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 % Computer : n017.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 18:55:00 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.42/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.42/1.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------