%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET558-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:43:25 PM UTC 2026
% Result : Unsatisfiable 5.90s 1.25s
% Output : Proof 5.90s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t110,axiom,
sF0 = operation(xf1),
introduced(definition) ).
cnf(f112,negated_conjecture,
operation(xf1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_1) ).
fof(f112_nnf,plain,
operation(xf1),
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
operation(xf1),
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
cnf(t4,plain,
operation(xf1) = true,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t121,plain,
operation(xf1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t673,plain,
sF0 = true,
inference(step,[status(thm)],[t110,t121]) ).
cnf(t122,plain,
true = sF0,
inference(orient,[status(thm)],[t673]) ).
cnf(t115,axiom,
sF5 = eq(cross_product(domain_of(xh),domain_of(xh)),domain_of(xf1)),
introduced(definition) ).
cnf(t112,axiom,
sF2 = domain_of(xh),
introduced(definition) ).
cnf(t132,plain,
domain_of(xh) = sF2,
inference(orient,[status(thm)],[t112]) ).
cnf(t729,plain,
sF5 = eq(cross_product(sF2,domain_of(xh)),domain_of(xf1)),
inference(step,[status(thm)],[t115,t132]) ).
cnf(t730,plain,
sF5 = eq(cross_product(sF2,sF2),domain_of(xf1)),
inference(step,[status(thm)],[t729,t132]) ).
cnf(t113,axiom,
sF3 = cross_product(domain_of(xh),domain_of(xh)),
introduced(definition) ).
cnf(t696,plain,
sF3 = cross_product(sF2,domain_of(xh)),
inference(step,[status(thm)],[t113,t132]) ).
cnf(t697,plain,
sF3 = cross_product(sF2,sF2),
inference(step,[status(thm)],[t696,t132]) ).
cnf(t149,plain,
cross_product(sF2,sF2) = sF3,
inference(orient,[status(thm)],[t697]) ).
cnf(t731,plain,
sF5 = eq(sF3,domain_of(xf1)),
inference(step,[status(thm)],[t730,t149]) ).
cnf(t114,axiom,
sF4 = domain_of(xf1),
introduced(definition) ).
cnf(t133,plain,
domain_of(xf1) = sF4,
inference(orient,[status(thm)],[t114]) ).
cnf(t732,plain,
sF5 = eq(sF3,sF4),
inference(step,[status(thm)],[t731,t133]) ).
cnf(f114,negated_conjecture,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_3) ).
fof(f114_nnf,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t30,plain,
eq(cross_product(domain_of(xh),domain_of(xh)),domain_of(xf1)) = false,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t715,plain,
eq(cross_product(sF2,domain_of(xh)),domain_of(xf1)) = false,
inference(step,[status(thm)],[t30,t132]) ).
cnf(t716,plain,
eq(cross_product(sF2,sF2),domain_of(xf1)) = false,
inference(step,[status(thm)],[t715,t132]) ).
cnf(t717,plain,
eq(sF3,domain_of(xf1)) = false,
inference(step,[status(thm)],[t716,t149]) ).
cnf(t718,plain,
eq(sF3,sF4) = false,
inference(step,[status(thm)],[t717,t133]) ).
cnf(t198,plain,
eq(sF3,sF4) = false,
inference(orient,[status(thm)],[t718]) ).
cnf(t733,plain,
sF5 = false,
inference(step,[status(thm)],[t732,t198]) ).
cnf(t214,plain,
false = sF5,
inference(orient,[status(thm)],[t733]) ).
cnf(t739,plain,
eq(sF3,sF4) = sF5,
inference(step,[status(thm)],[t198,t214]) ).
cnf(t222,plain,
eq(sF3,sF4) = sF5,
inference(orient,[status(thm)],[t739]) ).
cnf(t620,plain,
eq(sF3,sF3) = sF5,
inference(rw,[status(thm)],[t222]) ).
cnf(t5,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t683,plain,
eq(X1,X1) = sF0,
inference(step,[status(thm)],[t5,t122]) ).
cnf(t135,plain,
eq(X1,X1) = sF0,
inference(orient,[status(thm)],[t683]) ).
cnf(t916,plain,
sF0 = sF5,
inference(step,[status(thm)],[t620,t135]) ).
cnf(t638,plain,
sF5 = sF0,
inference(orient,[status(thm)],[t916]) ).
cnf(t919,plain,
false = sF0,
inference(step,[status(thm)],[t214,t638]) ).
cnf(t641,plain,
false = sF0,
inference(orient,[status(thm)],[t919]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c114]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t122]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t641]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET558-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:15:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.90/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.90/1.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------