%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 03:32:06 PM UTC 2026
% Result : Unsatisfiable 2.30s 0.80s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 16 RR)
% Number of literals : 44 ( 43 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
eq2(mul_idem(X),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t10,plain,
eqq(eq2(mul_idem(X1),bfalse),btrue) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t36,plain,
eqq(eq2(mul_idem(X1),bfalse),btrue) = efalse,
inference(orient,[status(thm)],[t10]) ).
cnf(t9,axiom,
eq(x22(X1,X1),X1) = mul_idem(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,plain,
eq(x22(X1,X1),X1) = mul_idem(X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t13,axiom,
x2(X1,x22(X2,X1)) = x22(s(X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
x2(X1,x22(X2,X1)) = x22(s(X2),X1),
inference(orient,[status(thm)],[t13]) ).
cnf(t6,axiom,
x22(z,X1) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
x22(z,X1) = z,
inference(orient,[status(thm)],[t6]) ).
cnf(t33,plain,
x22(s(z),X1) = x2(X1,z),
inference(cp,[status(thm)],[t31,t28]) ).
cnf(t45,plain,
x22(s(z),X1) = x2(X1,z),
inference(orient,[status(thm)],[t33]) ).
cnf(t46,plain,
x22(s(s(z)),X1) = x2(X1,x2(X1,z)),
inference(cp,[status(thm)],[t31,t45]) ).
cnf(t67,plain,
x2(X1,x2(X1,z)) = x22(s(s(z)),X1),
inference(orient,[status(thm)],[t46]) ).
cnf(t12,axiom,
x2(s(X1),X2) = s(x2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
s(x2(X1,X2)) = x2(s(X1),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t5,axiom,
x2(z,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
x2(z,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t20,plain,
x2(s(z),X1) = s(X1),
inference(cp,[status(thm)],[t19,t14]) ).
cnf(t40,plain,
x2(s(z),X1) = s(X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t42,plain,
x2(s(s(z)),X1) = s(s(X1)),
inference(cp,[status(thm)],[t19,t40]) ).
cnf(t49,plain,
x2(s(s(z)),X1) = s(s(X1)),
inference(orient,[status(thm)],[t42]) ).
cnf(t71,plain,
x22(s(s(z)),s(s(z))) = x2(s(s(z)),s(s(z))),
inference(cp,[status(thm)],[t67,t49]) ).
cnf(t156,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(step,[status(thm)],[t71,t49]) ).
cnf(t137,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(orient,[status(thm)],[t156]) ).
cnf(t140,plain,
mul_idem(s(s(z))) = eq(s(s(s(s(z)))),s(s(z))),
inference(cp,[status(thm)],[t27,t137]) ).
cnf(t11,axiom,
eq(s(X1),s(X2)) = eq(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
eq(s(X1),s(X2)) = eq(X1,X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t157,plain,
mul_idem(s(s(z))) = eq(s(s(s(z))),s(z)),
inference(step,[status(thm)],[t140,t23]) ).
cnf(t158,plain,
mul_idem(s(s(z))) = eq(s(s(z)),z),
inference(step,[status(thm)],[t157,t23]) ).
cnf(t7,axiom,
eq(s(X1),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
eq(s(X1),z) = bfalse,
inference(orient,[status(thm)],[t7]) ).
cnf(t159,plain,
mul_idem(s(s(z))) = bfalse,
inference(step,[status(thm)],[t158,t15]) ).
cnf(t141,plain,
mul_idem(s(s(z))) = bfalse,
inference(orient,[status(thm)],[t159]) ).
cnf(t142,plain,
efalse = eqq(eq2(bfalse,bfalse),btrue),
inference(cp,[status(thm)],[t36,t141]) ).
cnf(t1,axiom,
eq2(X1,X1) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t30,plain,
eq2(X1,X1) = btrue,
inference(orient,[status(thm)],[t1]) ).
cnf(t160,plain,
efalse = eqq(btrue,btrue),
inference(step,[status(thm)],[t142,t30]) ).
cnf(t4,plain,
eqq(X1,X1) = etrue,
introduced(definition) ).
cnf(t35,plain,
eqq(X1,X1) = etrue,
inference(orient,[status(thm)],[t4]) ).
cnf(t161,plain,
efalse = etrue,
inference(step,[status(thm)],[t160,t35]) ).
cnf(t143,plain,
efalse = etrue,
inference(orient,[status(thm)],[t161]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t143]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 23:40:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.30/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.30/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------