%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE055+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 01:51:30 PM UTC 2026
% Result : Theorem 6.07s 1.23s
% Output : Proof 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 67 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 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 : 94 ( 4 sgn 38 !; 1 ?)
% 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(t24,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t55,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t24]) ).
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(t8,plain,
multiplication(X1,one) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t28,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t57,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t55,t28]) ).
cnf(t300,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t57]) ).
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(t19,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t44,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(orient,[status(thm)],[t19]) ).
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(t25,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)],[t25]) ).
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(t10,plain,
multiplication(one,X1) = X1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t29,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t51,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t49,t29]) ).
cnf(t268,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t51]) ).
cnf(t603,plain,
multiplication(addition(one,domain(X1)),X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t44,t268]) ).
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(t12,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(t14,plain,
addition(X1,X2) = addition(X2,X1),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t34,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t14]) ).
cnf(t585,plain,
addition(one,domain(X1)) = one,
inference(step,[status(thm)],[t12,t34]) ).
cnf(t65,plain,
addition(one,domain(X1)) = one,
inference(orient,[status(thm)],[t585]) ).
cnf(t604,plain,
multiplication(one,X1) = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t603,t65]) ).
cnf(t605,plain,
X1 = multiplication(domain(X1),X1),
inference(step,[status(thm)],[t604,t29]) ).
cnf(t280,plain,
X1 = multiplication(domain(X1),X1),
inference(rw,[status(thm)],[t605]) ).
cnf(t281,plain,
multiplication(domain(X1),X1) = X1,
inference(orient,[status(thm)],[t280]) ).
cnf(t304,plain,
multiplication(domain(X1),addition(one,X1)) = addition(domain(X1),X1),
inference(cp,[status(thm)],[t300,t281]) ).
cnf(t613,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(step,[status(thm)],[t304,t34]) ).
cnf(t538,plain,
multiplication(domain(X1),addition(one,X1)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t613]) ).
cnf(t552,plain,
addition(X1,domain(X1)) = multiplication(domain(X1),addition(X1,one)),
inference(cp,[status(thm)],[t538,t34]) ).
cnf(t560,plain,
multiplication(domain(X1),addition(X1,one)) = addition(X1,domain(X1)),
inference(orient,[status(thm)],[t552]) ).
fof(f17,conjecture,
! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f17_neg,negated_conjecture,
~ ! [X0] :
( addition(X0,one) = one
=> addition(X0,domain(X0)) = domain(X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [X0] :
( addition(X0,domain(X0)) != domain(X0)
& addition(X0,one) = one ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( addition(sk0,domain(sk0)) != domain(sk0)
& addition(sk0,one) = one ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c18,plain,
addition(sk0,one) = one,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t3,plain,
addition(sk0,one) = one,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t68,plain,
addition(sk0,one) = one,
inference(orient,[status(thm)],[t3]) ).
cnf(t567,plain,
addition(sk0,domain(sk0)) = multiplication(domain(sk0),one),
inference(cp,[status(thm)],[t560,t68]) ).
cnf(t614,plain,
addition(sk0,domain(sk0)) = domain(sk0),
inference(step,[status(thm)],[t567,t28]) ).
cnf(t576,plain,
addition(sk0,domain(sk0)) = domain(sk0),
inference(orient,[status(thm)],[t614]) ).
cnf(c19,plain,
addition(sk0,domain(sk0)) != domain(sk0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
addition(sk0,domain(sk0)) != domain(sk0),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
domain(sk0) != domain(sk0),
inference(rw,[status(thm)],[goal_0,t576]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE055+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 18:48:35 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.07/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------