%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE085+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 : n012.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 01:51:34 PM UTC 2026
% Result : Theorem 2.76s 0.78s
% Output : Proof 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 3 sgn 26 !; 1 ?)
% 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(t13,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t66,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t13]) ).
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(t17,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t71,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
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(t29,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t74,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t71,t29]) ).
cnf(t219,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t74]) ).
fof(f14,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/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(t15,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t232,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t15,t66]) ).
cnf(t106,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t232]) ).
fof(f15,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/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(t114,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t236,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(step,[status(thm)],[t106,t114]) ).
cnf(t117,plain,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[t236]) ).
cnf(t248,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(step,[status(thm)],[t117,t66]) ).
cnf(t206,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(orient,[status(thm)],[t248]) ).
cnf(t221,plain,
addition(domain(X1),antidomain(X1)) = addition(domain(X1),one),
inference(cp,[status(thm)],[t219,t206]) ).
cnf(t254,plain,
one = addition(domain(X1),one),
inference(step,[status(thm)],[t221,t206]) ).
cnf(t255,plain,
one = addition(one,domain(X1)),
inference(step,[status(thm)],[t254,t66]) ).
cnf(t227,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t255]) ).
fof(f20,conjecture,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0] : addition(domain(X0),one) = one,
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0] : addition(domain(X0),one) != one,
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
addition(domain(sk0),one) != one,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f20_nnf]) ).
cnf(c21,plain,
addition(domain(sk0),one) != one,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
addition(domain(sk0),one) != one,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
addition(one,domain(sk0)) != one,
inference(rw,[status(thm)],[goal_0,t66]) ).
cnf(g0_1,plain,
one != one,
inference(rw,[status(thm)],[g0_0,t227]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 18:52:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.76/0.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/0.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------