%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN568-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 03:35:13 PM UTC 2026
% Result : Unsatisfiable 9.36s 1.77s
% Output : Proof 9.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 57 unt; 0 def)
% Number of atoms : 89 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 63 ( 6 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,negated_conjecture,
( ~ p11(X5,X4)
| ~ p10(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p10_6) ).
fof(f5_nnf,plain,
! [X4,X5] :
( ~ p11(X5,X4)
| ~ p10(X4,X5) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X4,X5] :
( ~ p11(X5,X4)
| ~ p10(X4,X5) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ p11(X1,X0)
| ~ p10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t15,plain,
or(not(p10(X1,X2)),not(p11(X2,X1))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t82,plain,
or(not(p10(X1,X2)),not(p11(X2,X1))) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f19,negated_conjecture,
( ~ p11(f5(f6(c12)),X6)
| ~ p10(X6,X8)
| p10(f4(X6,X7),f4(X8,X7))
| p3(X7,f6(c12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_20) ).
fof(f19_nnf,plain,
! [X7,X6,X8] :
( ~ p11(f5(f6(c12)),X6)
| ~ p10(X6,X8)
| p10(f4(X6,X7),f4(X8,X7))
| p3(X7,f6(c12)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X7,X6,X8] :
( ~ p11(f5(f6(c12)),X6)
| ~ p10(X6,X8)
| p10(f4(X6,X7),f4(X8,X7))
| p3(X7,f6(c12)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p11(f5(f6(c12)),X1)
| ~ p10(X1,X2)
| p10(f4(X1,X0),f4(X2,X0))
| p3(X0,f6(c12)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t30,plain,
ifeq(p10(X1,X2),true,ifeq(p11(f5(f6(c12)),X1),true,or(p3(X3,f6(c12)),p10(f4(X1,X3),f4(X2,X3))),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t49,plain,
ifeq(p10(X1,X2),true,ifeq(p11(f5(f6(c12)),X1),true,or(p3(X3,f6(c12)),p10(f4(X1,X3),f4(X2,X3))),true),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(f4,negated_conjecture,
( p11(X5,X4)
| p10(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_5) ).
fof(f4_nnf,plain,
! [X4,X5] :
( p11(X5,X4)
| p10(X4,X5) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X4,X5] :
( p11(X5,X4)
| p10(X4,X5) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( p11(X1,X0)
| p10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t12,plain,
or(p10(X1,X2),p11(X2,X1)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t81,plain,
or(p10(X1,X2),p11(X2,X1)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(f2,negated_conjecture,
~ p11(f9(c13),f9(c14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p11_3) ).
fof(f2_nnf,plain,
~ p11(f9(c13),f9(c14)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ p11(f9(c13),f9(c14)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ p11(f9(c13),f9(c14)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t9,plain,
p11(f9(c13),f9(c14)) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t99,plain,
p11(f9(c13),f9(c14)) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t100,plain,
true = or(p10(f9(c14),f9(c13)),false),
inference(cp,[status(thm)],[t81,t99]) ).
cnf(t2,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t32,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t228,plain,
true = p10(f9(c14),f9(c13)),
inference(step,[status(thm)],[t100,t32]) ).
cnf(t109,plain,
p10(f9(c14),f9(c13)) = true,
inference(orient,[status(thm)],[t228]) ).
cnf(t112,plain,
true = ifeq(true,true,ifeq(p11(f5(f6(c12)),f9(c14)),true,or(p3(X1,f6(c12)),p10(f4(f9(c14),X1),f4(f9(c13),X1))),true),true),
inference(cp,[status(thm)],[t49,t109]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t31,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t246,plain,
true = ifeq(p11(f5(f6(c12)),f9(c14)),true,or(p3(X1,f6(c12)),p10(f4(f9(c14),X1),f4(f9(c13),X1))),true),
inference(step,[status(thm)],[t112,t31]) ).
cnf(f3,negated_conjecture,
p11(f5(f6(c12)),f9(X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_4) ).
fof(f3_nnf,plain,
! [X16] : p11(f5(f6(c12)),f9(X16)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X16] : p11(f5(f6(c12)),f9(X16)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p11(f5(f6(c12)),f9(X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
p11(f5(f6(c12)),f9(X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t72,plain,
p11(f5(f6(c12)),f9(X1)) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t247,plain,
true = ifeq(true,true,or(p3(X1,f6(c12)),p10(f4(f9(c14),X1),f4(f9(c13),X1))),true),
inference(step,[status(thm)],[t246,t72]) ).
cnf(t248,plain,
true = or(p3(X1,f6(c12)),p10(f4(f9(c14),X1),f4(f9(c13),X1))),
inference(step,[status(thm)],[t247,t31]) ).
cnf(t148,plain,
or(p3(X1,f6(c12)),p10(f4(f9(c14),X1),f4(f9(c13),X1))) = true,
inference(orient,[status(thm)],[t248]) ).
cnf(f6,negated_conjecture,
~ p3(f6(f7(f8(c12))),f6(c12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p3_7) ).
fof(f6_nnf,plain,
~ p3(f6(f7(f8(c12))),f6(c12)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ p3(f6(f7(f8(c12))),f6(c12)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ p3(f6(f7(f8(c12))),f6(c12)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t13,plain,
p3(f6(f7(f8(c12))),f6(c12)) = false,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t87,plain,
p3(f6(f7(f8(c12))),f6(c12)) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(t149,plain,
true = or(false,p10(f4(f9(c14),f6(f7(f8(c12)))),f4(f9(c13),f6(f7(f8(c12)))))),
inference(cp,[status(thm)],[t148,t87]) ).
cnf(t4,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t33,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t261,plain,
true = p10(f4(f9(c14),f6(f7(f8(c12)))),f4(f9(c13),f6(f7(f8(c12))))),
inference(step,[status(thm)],[t149,t33]) ).
cnf(t192,plain,
p10(f4(f9(c14),f6(f7(f8(c12)))),f4(f9(c13),f6(f7(f8(c12))))) = true,
inference(orient,[status(thm)],[t261]) ).
cnf(t197,plain,
true = or(not(true),not(p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))))),
inference(cp,[status(thm)],[t82,t192]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t106,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t262,plain,
true = or(false,not(p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))))),
inference(step,[status(thm)],[t197,t106]) ).
cnf(t263,plain,
true = not(p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12)))))),
inference(step,[status(thm)],[t262,t33]) ).
cnf(f17,negated_conjecture,
p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_18) ).
fof(f17_nnf,plain,
p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t25,plain,
p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t66,plain,
p11(f4(f9(c13),f6(f7(f8(c12)))),f4(f9(c14),f6(f7(f8(c12))))) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t264,plain,
true = not(true),
inference(step,[status(thm)],[t263,t66]) ).
cnf(t265,plain,
true = false,
inference(step,[status(thm)],[t264,t106]) ).
cnf(t203,plain,
false = true,
inference(orient,[status(thm)],[t265]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c5,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t203]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN568-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n015.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 01:47:57 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.36/1.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.36/1.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------