%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN560-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 03:35:12 PM UTC 2026
% Result : Unsatisfiable 95.98s 22.59s
% Output : Proof 95.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 96 ( 76 unt; 0 def)
% Number of atoms : 136 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 153 ( 2 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,negated_conjecture,
( ~ p2(X22,X20)
| ~ p8(X22,X23)
| ~ p2(X23,X21)
| p8(X20,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_12) ).
fof(f11_nnf,plain,
! [X20,X21,X23,X22] :
( ~ p2(X22,X20)
| ~ p8(X22,X23)
| ~ p2(X23,X21)
| p8(X20,X21) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X20,X21,X23,X22] :
( ~ p2(X22,X20)
| ~ p8(X22,X23)
| ~ p2(X23,X21)
| p8(X20,X21) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p2(X3,X0)
| ~ p8(X3,X2)
| ~ p2(X2,X1)
| p8(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t21,plain,
ifeq(p2(X1,X2),true,ifeq(p8(X3,X1),true,ifeq(p2(X3,X4),true,p8(X4,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t61,plain,
ifeq(p2(X1,X2),true,ifeq(p8(X3,X1),true,ifeq(p2(X3,X4),true,p8(X4,X2),true),true),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f10,negated_conjecture,
~ p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p8_11) ).
fof(f10_nnf,plain,
~ p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t14,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))) = false,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t95,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f4(f5(c12,c14))))) = false,
inference(orient,[status(thm)],[t14]) ).
cnf(t100,plain,
true = ifeq(p2(X1,f6(c9,f4(f4(f5(c12,c14))))),true,ifeq(p8(X2,X1),true,ifeq(p2(X2,f6(c9,f4(c12))),true,false,true),true),true),
inference(cp,[status(thm)],[t61,t95]) ).
cnf(t67014,plain,
ifeq(p2(X1,f6(c9,f4(f4(f5(c12,c14))))),true,ifeq(p8(X2,X1),true,ifeq(p2(X2,f6(c9,f4(c12))),true,false,true),true),true) = true,
inference(orient,[status(thm)],[t100]) ).
cnf(f8,negated_conjecture,
( ~ p8(X26,X25)
| ~ p8(X24,X26)
| p8(X24,X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9) ).
fof(f8_nnf,plain,
! [X24,X25,X26] :
( ~ p8(X26,X25)
| ~ p8(X24,X26)
| p8(X24,X25) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X24,X25,X26] :
( ~ p8(X26,X25)
| ~ p8(X24,X26)
| p8(X24,X25) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p8(X2,X1)
| ~ p8(X0,X2)
| p8(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t16,plain,
ifeq(p8(X1,X2),true,ifeq(p8(X2,X3),true,p8(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t69,plain,
ifeq(p8(X1,X2),true,ifeq(p8(X2,X3),true,p8(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f9,negated_conjecture,
p8(f6(c9,f4(c12)),f6(c9,f4(f5(c12,c14)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_10) ).
fof(f9_nnf,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f5(c12,c14)))),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f5(c12,c14)))),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t13,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f5(c12,c14)))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t71,plain,
p8(f6(c9,f4(c12)),f6(c9,f4(f5(c12,c14)))) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t72,plain,
true = ifeq(true,true,ifeq(p8(f6(c9,f4(f5(c12,c14))),X1),true,p8(f6(c9,f4(c12)),X1),true),true),
inference(cp,[status(thm)],[t69,t71]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t67930,plain,
true = ifeq(p8(f6(c9,f4(f5(c12,c14))),X1),true,p8(f6(c9,f4(c12)),X1),true),
inference(step,[status(thm)],[t72,t22]) ).
cnf(t26923,plain,
ifeq(p8(f6(c9,f4(f5(c12,c14))),X1),true,p8(f6(c9,f4(c12)),X1),true) = true,
inference(orient,[status(thm)],[t67930]) ).
cnf(f14,negated_conjecture,
( p8(f6(X3,X4),f6(X3,f5(X4,f3(f7(c10)))))
| p2(X3,f3(c10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_15) ).
fof(f14_nnf,plain,
! [X3,X4] :
( p8(f6(X3,X4),f6(X3,f5(X4,f3(f7(c10)))))
| p2(X3,f3(c10)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X3,X4] :
( p8(f6(X3,X4),f6(X3,f5(X4,f3(f7(c10)))))
| p2(X3,f3(c10)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( p8(f6(X0,X1),f6(X0,f5(X1,f3(f7(c10)))))
| p2(X0,f3(c10)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t18,plain,
or(p2(X1,f3(c10)),p8(f6(X1,X2),f6(X1,f5(X2,f3(f7(c10)))))) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t79,plain,
or(p2(X1,f3(c10)),p8(f6(X1,X2),f6(X1,f5(X2,f3(f7(c10)))))) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(f1,negated_conjecture,
~ p2(c9,f3(c10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p2_2) ).
fof(f1_nnf,plain,
~ p2(c9,f3(c10)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ p2(c9,f3(c10)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ p2(c9,f3(c10)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t5,plain,
p2(c9,f3(c10)) = false,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t80,plain,
p2(c9,f3(c10)) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t93,plain,
true = or(false,p8(f6(c9,X1),f6(c9,f5(X1,f3(f7(c10)))))),
inference(cp,[status(thm)],[t79,t80]) ).
cnf(t2,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t24,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t67102,plain,
true = p8(f6(c9,X1),f6(c9,f5(X1,f3(f7(c10))))),
inference(step,[status(thm)],[t93,t24]) ).
cnf(t628,plain,
p8(f6(c9,X1),f6(c9,f5(X1,f3(f7(c10))))) = true,
inference(orient,[status(thm)],[t67102]) ).
cnf(t26924,plain,
true = ifeq(true,true,p8(f6(c9,f4(c12)),f6(c9,f5(f4(f5(c12,c14)),f3(f7(c10))))),true),
inference(cp,[status(thm)],[t26923,t628]) ).
cnf(t68239,plain,
true = p8(f6(c9,f4(c12)),f6(c9,f5(f4(f5(c12,c14)),f3(f7(c10))))),
inference(step,[status(thm)],[t26924,t22]) ).
cnf(t39060,plain,
p8(f6(c9,f4(c12)),f6(c9,f5(f4(f5(c12,c14)),f3(f7(c10))))) = true,
inference(orient,[status(thm)],[t68239]) ).
cnf(t67019,plain,
true = ifeq(p2(f6(c9,f5(f4(f5(c12,c14)),f3(f7(c10)))),f6(c9,f4(f4(f5(c12,c14))))),true,ifeq(true,true,ifeq(p2(f6(c9,f4(c12)),f6(c9,f4(c12))),true,false,true),true),true),
inference(cp,[status(thm)],[t67014,t39060]) ).
cnf(f7,negated_conjecture,
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_8) ).
fof(f7_nnf,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t15,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t51,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X1,X3),true,p2(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f0,negated_conjecture,
p2(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X0] : p2(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p2(X0,X0),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
p2(X1,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t25,plain,
p2(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t55,plain,
true = ifeq(p2(X1,X2),true,ifeq(true,true,p2(X2,X1),true),true),
inference(cp,[status(thm)],[t51,t25]) ).
cnf(t67069,plain,
true = ifeq(p2(X1,X2),true,p2(X2,X1),true),
inference(step,[status(thm)],[t55,t22]) ).
cnf(t143,plain,
ifeq(p2(X1,X2),true,p2(X2,X1),true) = true,
inference(orient,[status(thm)],[t67069]) ).
cnf(f13,negated_conjecture,
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f6(X14,X15),f6(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_14) ).
fof(f13_nnf,plain,
! [X14,X15,X16,X17] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f6(X14,X15),f6(X16,X17)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X14,X15,X16,X17] :
( ~ p2(X14,X16)
| ~ p2(X15,X17)
| p2(f6(X14,X15),f6(X16,X17)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p2(X0,X2)
| ~ p2(X1,X3)
| p2(f6(X0,X1),f6(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t20,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,p2(f6(X3,X1),f6(X4,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t37,plain,
ifeq(p2(X1,X2),true,ifeq(p2(X3,X4),true,p2(f6(X3,X1),f6(X4,X2)),true),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f3,negated_conjecture,
p2(f4(X9),f5(X9,f3(f7(c10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
! [X9] : p2(f4(X9),f5(X9,f3(f7(c10)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X9] : p2(f4(X9),f5(X9,f3(f7(c10)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p2(f4(X0),f5(X0,f3(f7(c10)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t9,plain,
p2(f4(X1),f5(X1,f3(f7(c10)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
p2(f4(X1),f5(X1,f3(f7(c10)))) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t40,plain,
true = ifeq(true,true,ifeq(p2(X1,X2),true,p2(f6(X1,f4(X3)),f6(X2,f5(X3,f3(f7(c10))))),true),true),
inference(cp,[status(thm)],[t37,t26]) ).
cnf(t67189,plain,
true = ifeq(p2(X1,X2),true,p2(f6(X1,f4(X3)),f6(X2,f5(X3,f3(f7(c10))))),true),
inference(step,[status(thm)],[t40,t22]) ).
cnf(t1986,plain,
ifeq(p2(X1,X2),true,p2(f6(X1,f4(X3)),f6(X2,f5(X3,f3(f7(c10))))),true) = true,
inference(orient,[status(thm)],[t67189]) ).
cnf(t1987,plain,
true = ifeq(true,true,p2(f6(X1,f4(X2)),f6(X1,f5(X2,f3(f7(c10))))),true),
inference(cp,[status(thm)],[t1986,t25]) ).
cnf(t67211,plain,
true = p2(f6(X1,f4(X2)),f6(X1,f5(X2,f3(f7(c10))))),
inference(step,[status(thm)],[t1987,t22]) ).
cnf(t2454,plain,
p2(f6(X1,f4(X2)),f6(X1,f5(X2,f3(f7(c10))))) = true,
inference(orient,[status(thm)],[t67211]) ).
cnf(t2455,plain,
true = ifeq(true,true,p2(f6(X1,f5(X2,f3(f7(c10)))),f6(X1,f4(X2))),true),
inference(cp,[status(thm)],[t143,t2454]) ).
cnf(t67212,plain,
true = p2(f6(X1,f5(X2,f3(f7(c10)))),f6(X1,f4(X2))),
inference(step,[status(thm)],[t2455,t22]) ).
cnf(t2472,plain,
p2(f6(X1,f5(X2,f3(f7(c10)))),f6(X1,f4(X2))) = true,
inference(orient,[status(thm)],[t67212]) ).
cnf(t68676,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(p2(f6(c9,f4(c12)),f6(c9,f4(c12))),true,false,true),true),true),
inference(step,[status(thm)],[t67019,t2472]) ).
cnf(t68677,plain,
true = ifeq(true,true,ifeq(p2(f6(c9,f4(c12)),f6(c9,f4(c12))),true,false,true),true),
inference(step,[status(thm)],[t68676,t22]) ).
cnf(t68678,plain,
true = ifeq(p2(f6(c9,f4(c12)),f6(c9,f4(c12))),true,false,true),
inference(step,[status(thm)],[t68677,t22]) ).
cnf(t68679,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t68678,t25]) ).
cnf(t68680,plain,
true = false,
inference(step,[status(thm)],[t68679,t22]) ).
cnf(t67023,plain,
false = true,
inference(orient,[status(thm)],[t68680]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t67023]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN560-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.37 % Computer : n020.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Fri Sep 25 01:46:59 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 95.98/22.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.98/22.59 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------