%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE083+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 : n018.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 5.83s 1.24s
% Output : Proof 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 32 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(t22,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)],[t22]) ).
fof(f12,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/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(t12,plain,
multiplication(antidomain(X1),X1) = zero,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t57,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t12]) ).
cnf(t60,plain,
multiplication(addition(X1,antidomain(X2)),X2) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t49,t57]) ).
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(t30,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t621,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(step,[status(thm)],[t60,t30]) ).
cnf(t540,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(orient,[status(thm)],[t621]) ).
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]) ).
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]) ).
cnf(t567,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)],[t567]) ).
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(t571,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)],[t571]) ).
cnf(t583,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)],[t583]) ).
cnf(t541,plain,
multiplication(domain(X1),X1) = multiplication(one,X1),
inference(cp,[status(thm)],[t540,t206]) ).
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(t28,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t622,plain,
multiplication(domain(X1),X1) = X1,
inference(step,[status(thm)],[t541,t28]) ).
cnf(t556,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t622]) ).
fof(f20,conjecture,
! [X0] : X0 = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0] : X0 = multiplication(domain(X0),X0),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0] : X0 != multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
sk0 != multiplication(domain(sk0),sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f20_nnf]) ).
cnf(c21,plain,
sk0 != multiplication(domain(sk0),sk0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(domain(sk0),sk0) != sk0,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
sk0 != sk0,
inference(rw,[status(thm)],[goal_0,t556]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE083+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 18:55:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.83/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.83/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------