%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:51:35 PM UTC 2026
% Result : Theorem 5.71s 6.26s
% Output : Proof 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 43 unt; 0 def)
% Number of atoms : 65 ( 57 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 6 |; 4 &)
% ( 1 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/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(t73,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t25]) ).
fof(f12,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/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(t65,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t12]) ).
cnf(t79,plain,
multiplication(addition(X1,antidomain(X2)),X2) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t73,t65]) ).
fof(f2,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/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(t33,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t665,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(step,[status(thm)],[t79,t33]) ).
cnf(t574,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(orient,[status(thm)],[t665]) ).
fof(f11,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f11_nnf,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi12,axiom,
ifeq(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f20,conjecture,
! [X0,X1] :
( multiplication(domain(X0),X1) = zero
<= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20_neg,negated_conjecture,
~ ! [X0,X1] :
( multiplication(domain(X0),X1) = zero
<= addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f20_nnf,plain,
? [X0,X1] :
( multiplication(domain(X0),X1) != zero
& addition(domain(X0),antidomain(X1)) = antidomain(X1) ),
inference(nnf_transformation,[status(thm)],[f20_neg]) ).
fof(f20_sk,plain,
( multiplication(domain(sk0),sk1) != zero
& addition(domain(sk0),antidomain(sk1)) = antidomain(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f20_nnf]) ).
cnf(c21,plain,
addition(domain(sk0),antidomain(sk1)) = antidomain(sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi19,negated_conjecture,
addition(domain(sk0),antidomain(sk1)) = antidomain(sk1),
inference(equality_encoding,[status(esa)],[c21]) ).
fof(f15,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/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(hi20,axiom,
domain(X0) = antidomain(antidomain(X0)),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h5,plain,
leq(antidomain(antidomain(sk0)),antidomain(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi19,hi20]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t19,plain,
addition(antidomain(antidomain(sk0)),antidomain(sk1)) = antidomain(sk1),
inference(hyper_resolution,[status(thm)],[hi11,h5]) ).
cnf(t9,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t38,plain,
antidomain(antidomain(X1)) = domain(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t607,plain,
addition(domain(sk0),antidomain(sk1)) = antidomain(sk1),
inference(step,[status(thm)],[t19,t38]) ).
cnf(t45,plain,
addition(domain(sk0),antidomain(sk1)) = antidomain(sk1),
inference(orient,[status(thm)],[t607]) ).
cnf(t576,plain,
multiplication(domain(sk0),sk1) = multiplication(antidomain(sk1),sk1),
inference(cp,[status(thm)],[t574,t45]) ).
cnf(t666,plain,
multiplication(domain(sk0),sk1) = zero,
inference(step,[status(thm)],[t576,t65]) ).
cnf(t595,plain,
multiplication(domain(sk0),sk1) = zero,
inference(orient,[status(thm)],[t666]) ).
cnf(c22,plain,
multiplication(domain(sk0),sk1) != zero,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
multiplication(domain(sk0),sk1) != zero,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t595]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 18:53:56 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.71/6.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/6.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------