%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN567-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 03:35:13 PM UTC 2026
% Result : Unsatisfiable 15.88s 2.43s
% Output : Proof 15.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 54 unt; 0 def)
% Number of atoms : 82 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 35 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,negated_conjecture,
( ~ p2(f6(f8(X3)),X3)
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f4(c10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_19) ).
fof(f18_nnf,plain,
! [X3] :
( ~ p2(f6(f8(X3)),X3)
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f4(c10))) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X3] :
( ~ p2(f6(f8(X3)),X3)
| p2(X3,f3(f7(f7(f7(f4(c10))))))
| p2(X3,f3(f7(f7(f4(c10)))))
| p2(X3,f3(f7(f4(c10))))
| p2(X3,f3(f4(c10))) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ p2(f6(f8(X0)),X0)
| p2(X0,f3(f7(f7(f7(f4(c10))))))
| p2(X0,f3(f7(f7(f4(c10)))))
| p2(X0,f3(f7(f4(c10))))
| p2(X0,f3(f4(c10))) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t27,plain,
ifeq(p2(f6(f8(X1)),X1),true,or(p2(X1,f3(f4(c10))),or(p2(X1,f3(f7(f4(c10)))),or(p2(X1,f3(f7(f7(f4(c10))))),p2(X1,f3(f7(f7(f7(f4(c10))))))))),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t57,plain,
ifeq(p2(f6(f8(X1)),X1),true,or(p2(X1,f3(f4(c10))),or(p2(X1,f3(f7(f4(c10)))),or(p2(X1,f3(f7(f7(f4(c10))))),p2(X1,f3(f7(f7(f7(f4(c10))))))))),true) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(f3,negated_conjecture,
~ p2(f6(c9),f3(f4(c10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_4) ).
fof(f3_nnf,plain,
~ p2(f6(c9),f3(f4(c10))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ p2(f6(c9),f3(f4(c10))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ p2(f6(c9),f3(f4(c10))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t8,plain,
p2(f6(c9),f3(f4(c10))) = false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t110,plain,
p2(f6(c9),f3(f4(c10))) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t119,plain,
true = ifeq(p2(f6(f8(f6(c9))),f6(c9)),true,or(false,or(p2(f6(c9),f3(f7(f4(c10)))),or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10))))))))),true),
inference(cp,[status(thm)],[t57,t110]) ).
cnf(f9,negated_conjecture,
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
! [X8,X9] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X8,X9] :
( ~ p5(X8,X9)
| p2(f6(X8),f6(X9)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ p5(X0,X1)
| p2(f6(X0),f6(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t18,plain,
ifeq(p5(X1,X2),true,p2(f6(X1),f6(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t62,plain,
ifeq(p5(X1,X2),true,p2(f6(X1),f6(X2)),true) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(f2,negated_conjecture,
p5(f8(f6(X17)),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_3) ).
fof(f2_nnf,plain,
! [X17] : p5(f8(f6(X17)),X17),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X17] : p5(f8(f6(X17)),X17),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p5(f8(f6(X0)),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
p5(f8(f6(X1)),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t69,plain,
p5(f8(f6(X1)),X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t73,plain,
true = ifeq(true,true,p2(f6(f8(f6(X1))),f6(X1)),true),
inference(cp,[status(thm)],[t62,t69]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t329,plain,
true = p2(f6(f8(f6(X1))),f6(X1)),
inference(step,[status(thm)],[t73,t28]) ).
cnf(t122,plain,
p2(f6(f8(f6(X1))),f6(X1)) = true,
inference(orient,[status(thm)],[t329]) ).
cnf(t353,plain,
true = ifeq(true,true,or(false,or(p2(f6(c9),f3(f7(f4(c10)))),or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10))))))))),true),
inference(step,[status(thm)],[t119,t122]) ).
cnf(t354,plain,
true = or(false,or(p2(f6(c9),f3(f7(f4(c10)))),or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10))))))))),
inference(step,[status(thm)],[t353,t28]) ).
cnf(t2,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t30,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t355,plain,
true = or(p2(f6(c9),f3(f7(f4(c10)))),or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10)))))))),
inference(step,[status(thm)],[t354,t30]) ).
cnf(f4,negated_conjecture,
~ p2(f6(c9),f3(f7(f4(c10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_5) ).
fof(f4_nnf,plain,
~ p2(f6(c9),f3(f7(f4(c10)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ p2(f6(c9),f3(f7(f4(c10)))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ p2(f6(c9),f3(f7(f4(c10)))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
p2(f6(c9),f3(f7(f4(c10)))) = false,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t99,plain,
p2(f6(c9),f3(f7(f4(c10)))) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t356,plain,
true = or(false,or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10)))))))),
inference(step,[status(thm)],[t355,t99]) ).
cnf(t357,plain,
true = or(p2(f6(c9),f3(f7(f7(f4(c10))))),p2(f6(c9),f3(f7(f7(f7(f4(c10))))))),
inference(step,[status(thm)],[t356,t30]) ).
cnf(f5,negated_conjecture,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_6) ).
fof(f5_nnf,plain,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ p2(f6(c9),f3(f7(f7(f4(c10))))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
p2(f6(c9),f3(f7(f7(f4(c10))))) = false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t88,plain,
p2(f6(c9),f3(f7(f7(f4(c10))))) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t358,plain,
true = or(false,p2(f6(c9),f3(f7(f7(f7(f4(c10))))))),
inference(step,[status(thm)],[t357,t88]) ).
cnf(t359,plain,
true = p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
inference(step,[status(thm)],[t358,t30]) ).
cnf(f11,negated_conjecture,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_12) ).
fof(f11_nnf,plain,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ p2(f6(c9),f3(f7(f7(f7(f4(c10)))))),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t11,plain,
p2(f6(c9),f3(f7(f7(f7(f4(c10)))))) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t77,plain,
p2(f6(c9),f3(f7(f7(f7(f4(c10)))))) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t360,plain,
true = false,
inference(step,[status(thm)],[t359,t77]) ).
cnf(t312,plain,
false = true,
inference(orient,[status(thm)],[t360]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c4,c5,c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t312]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN567-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n019.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 : Fri Sep 25 01:44:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.88/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.88/2.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------