%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE069+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 : n004.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 01:51:32 PM UTC 2026
% Result : Theorem 8.24s 11.65s
% Output : Proof 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 77 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 4 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f7_nnf,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t22,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t53,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
fof(f12,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f12_nnf,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t17,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t42,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t17]) ).
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(t23,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t47,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t23]) ).
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(t8,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t27,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t49,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t47,t27]) ).
cnf(t224,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t49]) ).
cnf(t3723,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t42,t224]) ).
fof(f14,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
fof(f14_nnf,plain,
! [X0] : addition(domain(X0),one) = one,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X0] : addition(domain(X0),one) = one,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t10,plain,
addition(domain(X1),one) = 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(t12,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t32,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t12]) ).
cnf(t3709,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t10,t32]) ).
cnf(t63,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t3709]) ).
cnf(t3724,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t3723,t63]) ).
cnf(t3725,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t3724,t27]) ).
cnf(t235,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t3725]) ).
cnf(t236,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t235]) ).
cnf(t244,plain,
multiplication(domain(X1),addition(X1,X2)) = addition(X1,multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t53,t236]) ).
cnf(t754,plain,
addition(X1,multiplication(domain(X1),X2)) = multiplication(domain(X1),addition(X1,X2)),
inference(orient,[status(thm)],[t244]) ).
fof(f13,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f13_nnf,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t16,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t76,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(orient,[status(thm)],[t16]) ).
cnf(t78,plain,
domain(multiplication(one,X1)) = domain(domain(X1)),
inference(cp,[status(thm)],[t76,t27]) ).
cnf(t3711,plain,
domain(X1) = domain(domain(X1)),
inference(step,[status(thm)],[t78,t27]) ).
cnf(t104,plain,
domain(domain(X1)) = domain(X1),
inference(orient,[status(thm)],[t3711]) ).
cnf(t764,plain,
multiplication(domain(domain(X1)),addition(domain(X1),X2)) = addition(domain(X1),multiplication(domain(X1),X2)),
inference(cp,[status(thm)],[t754,t104]) ).
cnf(t3778,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = addition(domain(X1),multiplication(domain(X1),X2)),
inference(step,[status(thm)],[t764,t104]) ).
fof(f5,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/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(t6,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t26,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t55,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t53,t26]) ).
cnf(t254,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t55]) ).
cnf(t3779,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = multiplication(domain(X1),addition(one,X2)),
inference(step,[status(thm)],[t3778,t254]) ).
cnf(t3686,plain,
multiplication(domain(X1),addition(domain(X1),X2)) = multiplication(domain(X1),addition(one,X2)),
inference(orient,[status(thm)],[t3779]) ).
fof(f17,conjecture,
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) != domain(X0),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
multiplication(domain(sk0),addition(domain(sk0),domain(sk1))) != domain(sk0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f17_nnf]) ).
cnf(c18,plain,
multiplication(domain(sk0),addition(domain(sk0),domain(sk1))) != domain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(domain(sk0),addition(domain(sk0),domain(sk1))) != domain(sk0),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
multiplication(domain(sk0),addition(one,domain(sk1))) != domain(sk0),
inference(rw,[status(thm)],[goal_0,t3686]) ).
cnf(g0_1,plain,
multiplication(domain(sk0),one) != domain(sk0),
inference(rw,[status(thm)],[g0_0,t63]) ).
cnf(g0_2,plain,
domain(sk0) != domain(sk0),
inference(rw,[status(thm)],[g0_1,t26]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/10.40 % Computer : n004.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Wed Sep 23 18:50:32 UTC 2026
% 0.15/10.40 % CPUTime :
% 0.15/10.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.24/11.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.24/11.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------