%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN063-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 03:33:40 PM UTC 2026
% Result : Unsatisfiable 3.08s 1.20s
% Output : Proof 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 37 unt; 0 def)
% Number of atoms : 53 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 25 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,negated_conjecture,
( big_p(Y)
| big_p(c)
| big_p(X)
| ~ big_p(a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( big_p(Y)
| big_p(c)
| big_p(X)
| ~ big_p(a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( big_p(Y)
| big_p(c)
| big_p(X)
| ~ big_p(a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( big_p(X1)
| big_p(c)
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t9,plain,
ifeq(big_p(a),true,or(big_p(X1),or(big_p(c),big_p(X2))),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f0,negated_conjecture,
big_p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
big_p(a),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
big_p(a),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t0,plain,
big_p(a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t16,plain,
big_p(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t42,plain,
ifeq(true,true,or(big_p(X1),or(big_p(c),big_p(X2))),true) = true,
inference(step,[status(thm)],[t9,t16]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t43,plain,
or(big_p(X1),or(big_p(c),big_p(X2))) = true,
inference(step,[status(thm)],[t42,t15]) ).
cnf(t19,plain,
or(big_p(X1),or(big_p(c),big_p(X2))) = true,
inference(orient,[status(thm)],[t43]) ).
cnf(f3,negated_conjecture,
~ big_p(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
~ big_p(c),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ big_p(c),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ big_p(c),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
big_p(c) = false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
big_p(c) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t52,plain,
or(big_p(X1),or(false,big_p(X2))) = true,
inference(step,[status(thm)],[t19,t26]) ).
cnf(t4,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t14,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t53,plain,
or(big_p(X1),big_p(X2)) = true,
inference(step,[status(thm)],[t52,t14]) ).
cnf(t28,plain,
or(big_p(X1),big_p(X2)) = true,
inference(rw,[status(thm)],[t53]) ).
cnf(t37,plain,
or(big_p(X1),big_p(X2)) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t12,axiom,
sFlat0 = big_p(c),
introduced(definition) ).
cnf(t56,plain,
sFlat0 = false,
inference(step,[status(thm)],[t12,t26]) ).
cnf(t30,plain,
false = sFlat0,
inference(orient,[status(thm)],[t56]) ).
cnf(t57,plain,
big_p(c) = sFlat0,
inference(step,[status(thm)],[t26,t30]) ).
cnf(t31,plain,
big_p(c) = sFlat0,
inference(orient,[status(thm)],[t57]) ).
cnf(t38,plain,
true = or(sFlat0,big_p(X1)),
inference(cp,[status(thm)],[t37,t31]) ).
cnf(t60,plain,
or(sFlat0,X1) = X1,
inference(step,[status(thm)],[t14,t30]) ).
cnf(t34,plain,
or(sFlat0,X1) = X1,
inference(rw,[status(thm)],[t60]) ).
cnf(t36,plain,
or(sFlat0,X1) = X1,
inference(orient,[status(thm)],[t34]) ).
cnf(t61,plain,
true = big_p(X1),
inference(step,[status(thm)],[t38,t36]) ).
cnf(t40,plain,
big_p(X1) = true,
inference(orient,[status(thm)],[t61]) ).
cnf(goal_0,negated_conjecture,
big_p(c) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN063-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:00:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.08/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------