%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD030-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 01:14:58 PM UTC 2026
% Result : Unsatisfiable 9.61s 1.81s
% Output : Proof 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 58 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 22 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 36 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f24,axiom,
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
fof(f24_nnf,plain,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t34,plain,
ifeq(defined(X1),true,ifeq(equalish(X2,X3),true,equalish(multiply(X2,X1),multiply(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t50,plain,
ifeq(defined(X1),true,ifeq(equalish(X2,X3),true,equalish(multiply(X2,X1),multiply(X3,X1)),true),true) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(f31,negated_conjecture,
~ equalish(multiply(d,b),multiply(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_not_equal_to_multiply_5) ).
fof(f31_nnf,plain,
~ equalish(multiply(d,b),multiply(a,b)),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ equalish(multiply(d,b),multiply(a,b)),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ equalish(multiply(d,b),multiply(a,b)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t12,plain,
equalish(multiply(d,b),multiply(a,b)) = false,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t231,plain,
equalish(multiply(d,b),multiply(a,b)) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t241,plain,
true = ifeq(defined(b),true,ifeq(equalish(d,a),true,false,true),true),
inference(cp,[status(thm)],[t50,t231]) ).
cnf(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f28_nnf,plain,
defined(b),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(t2,plain,
defined(b) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t99,plain,
defined(b) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t2453,plain,
true = ifeq(true,true,ifeq(equalish(d,a),true,false,true),true),
inference(step,[status(thm)],[t241,t99]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t39,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t2454,plain,
true = ifeq(equalish(d,a),true,false,true),
inference(step,[status(thm)],[t2453,t39]) ).
cnf(f21,axiom,
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f21_nnf,plain,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t16,plain,
ifeq(equalish(X1,X2),true,equalish(X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t61,plain,
ifeq(equalish(X1,X2),true,equalish(X2,X1),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f30,negated_conjecture,
equalish(a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_d_4) ).
fof(f30_nnf,plain,
equalish(a,d),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
equalish(a,d),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(t5,plain,
equalish(a,d) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t219,plain,
equalish(a,d) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t220,plain,
true = ifeq(true,true,equalish(d,a),true),
inference(cp,[status(thm)],[t61,t219]) ).
cnf(t2362,plain,
true = equalish(d,a),
inference(step,[status(thm)],[t220,t39]) ).
cnf(t444,plain,
equalish(d,a) = true,
inference(orient,[status(thm)],[t2362]) ).
cnf(t2455,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t2454,t444]) ).
cnf(t2456,plain,
true = false,
inference(step,[status(thm)],[t2455,t39]) ).
cnf(t2343,plain,
false = true,
inference(orient,[status(thm)],[t2456]) ).
cnf(f26,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
fof(f26_nnf,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c26,c31]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2343]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD030-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 10:44:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.61/1.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.61/1.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------