%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN005-1.010 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 03:33:18 PM UTC 2026
% Result : Unsatisfiable 5.58s 1.20s
% Output : Proof 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 83 unt; 0 def)
% Number of atoms : 123 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 156 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,negated_conjecture,
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjunction) ).
fof(f0_nnf,plain,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ p_10(X10,X1)
| ~ p_9(X9,X10)
| ~ p_8(X8,X9)
| ~ p_7(X7,X8)
| ~ p_6(X6,X7)
| ~ p_5(X5,X6)
| ~ p_4(X4,X5)
| ~ p_3(X3,X4)
| ~ p_2(X2,X3)
| ~ p_1(X1,X2) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ p_10(X9,X0)
| ~ p_9(X8,X9)
| ~ p_8(X7,X8)
| ~ p_7(X6,X7)
| ~ p_6(X5,X6)
| ~ p_5(X4,X5)
| ~ p_4(X3,X4)
| ~ p_3(X2,X3)
| ~ p_2(X1,X2)
| ~ p_1(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t11,plain,
ifeq(p_1(X1,X2),true,ifeq(p_2(X2,X3),true,ifeq(p_3(X3,X4),true,ifeq(p_4(X4,X5),true,ifeq(p_5(X5,X6),true,ifeq(p_6(X6,X7),true,ifeq(p_7(X7,X8),true,ifeq(p_8(X8,X9),true,ifeq(p_9(X9,X10),true,ifeq(p_10(X10,X1),true,false,true),true),true),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
ifeq(p_1(X1,X2),true,ifeq(p_2(X2,X3),true,ifeq(p_3(X3,X4),true,ifeq(p_4(X4,X5),true,ifeq(p_5(X5,X6),true,ifeq(p_6(X6,X7),true,ifeq(p_7(X7,X8),true,ifeq(p_8(X8,X9),true,ifeq(p_9(X9,X10),true,ifeq(p_10(X10,X1),true,false,true),true),true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(f1,negated_conjecture,
p_1(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_1) ).
fof(f1_nnf,plain,
p_1(a,a),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
p_1(a,a),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t0,plain,
p_1(a,a) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t14,plain,
p_1(a,a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t15,plain,
true = ifeq(true,true,ifeq(p_2(a,X1),true,ifeq(p_3(X1,X2),true,ifeq(p_4(X2,X3),true,ifeq(p_5(X3,X4),true,ifeq(p_6(X4,X5),true,ifeq(p_7(X5,X6),true,ifeq(p_8(X6,X7),true,ifeq(p_9(X7,X8),true,ifeq(p_10(X8,a),true,false,true),true),true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t13,t14]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t93,plain,
true = ifeq(p_2(a,X1),true,ifeq(p_3(X1,X2),true,ifeq(p_4(X2,X3),true,ifeq(p_5(X3,X4),true,ifeq(p_6(X4,X5),true,ifeq(p_7(X5,X6),true,ifeq(p_8(X6,X7),true,ifeq(p_9(X7,X8),true,ifeq(p_10(X8,a),true,false,true),true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t15,t12]) ).
cnf(t34,plain,
ifeq(p_2(a,X1),true,ifeq(p_3(X1,X2),true,ifeq(p_4(X2,X3),true,ifeq(p_5(X3,X4),true,ifeq(p_6(X4,X5),true,ifeq(p_7(X5,X6),true,ifeq(p_8(X6,X7),true,ifeq(p_9(X7,X8),true,ifeq(p_10(X8,a),true,false,true),true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t93]) ).
cnf(f2,negated_conjecture,
p_2(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_2) ).
fof(f2_nnf,plain,
p_2(a,a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
p_2(a,a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t2,plain,
p_2(a,a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t16,plain,
p_2(a,a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t35,plain,
true = ifeq(true,true,ifeq(p_3(a,X1),true,ifeq(p_4(X1,X2),true,ifeq(p_5(X2,X3),true,ifeq(p_6(X3,X4),true,ifeq(p_7(X4,X5),true,ifeq(p_8(X5,X6),true,ifeq(p_9(X6,X7),true,ifeq(p_10(X7,a),true,false,true),true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t34,t16]) ).
cnf(t94,plain,
true = ifeq(p_3(a,X1),true,ifeq(p_4(X1,X2),true,ifeq(p_5(X2,X3),true,ifeq(p_6(X3,X4),true,ifeq(p_7(X4,X5),true,ifeq(p_8(X5,X6),true,ifeq(p_9(X6,X7),true,ifeq(p_10(X7,a),true,false,true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t35,t12]) ).
cnf(t44,plain,
ifeq(p_3(a,X1),true,ifeq(p_4(X1,X2),true,ifeq(p_5(X2,X3),true,ifeq(p_6(X3,X4),true,ifeq(p_7(X4,X5),true,ifeq(p_8(X5,X6),true,ifeq(p_9(X6,X7),true,ifeq(p_10(X7,a),true,false,true),true),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t94]) ).
cnf(f4,negated_conjecture,
p_4(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_4) ).
fof(f4_nnf,plain,
p_4(a,a),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p_4(a,a),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(t4,plain,
p_4(a,a) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t20,plain,
p_4(a,a) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t46,plain,
true = ifeq(p_3(a,a),true,ifeq(true,true,ifeq(p_5(a,X1),true,ifeq(p_6(X1,X2),true,ifeq(p_7(X2,X3),true,ifeq(p_8(X3,X4),true,ifeq(p_9(X4,X5),true,ifeq(p_10(X5,a),true,false,true),true),true),true),true),true),true),true),
inference(cp,[status(thm)],[t44,t20]) ).
cnf(f3,negated_conjecture,
p_3(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_3) ).
fof(f3_nnf,plain,
p_3(a,a),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
p_3(a,a),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t3,plain,
p_3(a,a) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t18,plain,
p_3(a,a) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t95,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(p_5(a,X1),true,ifeq(p_6(X1,X2),true,ifeq(p_7(X2,X3),true,ifeq(p_8(X3,X4),true,ifeq(p_9(X4,X5),true,ifeq(p_10(X5,a),true,false,true),true),true),true),true),true),true),true),
inference(step,[status(thm)],[t46,t18]) ).
cnf(t96,plain,
true = ifeq(true,true,ifeq(p_5(a,X1),true,ifeq(p_6(X1,X2),true,ifeq(p_7(X2,X3),true,ifeq(p_8(X3,X4),true,ifeq(p_9(X4,X5),true,ifeq(p_10(X5,a),true,false,true),true),true),true),true),true),true),
inference(step,[status(thm)],[t95,t12]) ).
cnf(t97,plain,
true = ifeq(p_5(a,X1),true,ifeq(p_6(X1,X2),true,ifeq(p_7(X2,X3),true,ifeq(p_8(X3,X4),true,ifeq(p_9(X4,X5),true,ifeq(p_10(X5,a),true,false,true),true),true),true),true),true),
inference(step,[status(thm)],[t96,t12]) ).
cnf(t55,plain,
ifeq(p_5(a,X1),true,ifeq(p_6(X1,X2),true,ifeq(p_7(X2,X3),true,ifeq(p_8(X3,X4),true,ifeq(p_9(X4,X5),true,ifeq(p_10(X5,a),true,false,true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t97]) ).
cnf(f6,negated_conjecture,
p_6(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_6) ).
fof(f6_nnf,plain,
p_6(a,a),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
p_6(a,a),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t6,plain,
p_6(a,a) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
p_6(a,a) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t57,plain,
true = ifeq(p_5(a,a),true,ifeq(true,true,ifeq(p_7(a,X1),true,ifeq(p_8(X1,X2),true,ifeq(p_9(X2,X3),true,ifeq(p_10(X3,a),true,false,true),true),true),true),true),true),
inference(cp,[status(thm)],[t55,t26]) ).
cnf(f5,negated_conjecture,
p_5(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_5) ).
fof(f5_nnf,plain,
p_5(a,a),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p_5(a,a),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t5,plain,
p_5(a,a) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t22,plain,
p_5(a,a) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t99,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(p_7(a,X1),true,ifeq(p_8(X1,X2),true,ifeq(p_9(X2,X3),true,ifeq(p_10(X3,a),true,false,true),true),true),true),true),true),
inference(step,[status(thm)],[t57,t22]) ).
cnf(t100,plain,
true = ifeq(true,true,ifeq(p_7(a,X1),true,ifeq(p_8(X1,X2),true,ifeq(p_9(X2,X3),true,ifeq(p_10(X3,a),true,false,true),true),true),true),true),
inference(step,[status(thm)],[t99,t12]) ).
cnf(t101,plain,
true = ifeq(p_7(a,X1),true,ifeq(p_8(X1,X2),true,ifeq(p_9(X2,X3),true,ifeq(p_10(X3,a),true,false,true),true),true),true),
inference(step,[status(thm)],[t100,t12]) ).
cnf(t69,plain,
ifeq(p_7(a,X1),true,ifeq(p_8(X1,X2),true,ifeq(p_9(X2,X3),true,ifeq(p_10(X3,a),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t101]) ).
cnf(f8,negated_conjecture,
p_8(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_8) ).
fof(f8_nnf,plain,
p_8(a,a),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
p_8(a,a),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t8,plain,
p_8(a,a) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t32,plain,
p_8(a,a) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t71,plain,
true = ifeq(p_7(a,a),true,ifeq(true,true,ifeq(p_9(a,X1),true,ifeq(p_10(X1,a),true,false,true),true),true),true),
inference(cp,[status(thm)],[t69,t32]) ).
cnf(f7,negated_conjecture,
p_7(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_7) ).
fof(f7_nnf,plain,
p_7(a,a),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
p_7(a,a),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t7,plain,
p_7(a,a) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t24,plain,
p_7(a,a) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t102,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(p_9(a,X1),true,ifeq(p_10(X1,a),true,false,true),true),true),true),
inference(step,[status(thm)],[t71,t24]) ).
cnf(t103,plain,
true = ifeq(true,true,ifeq(p_9(a,X1),true,ifeq(p_10(X1,a),true,false,true),true),true),
inference(step,[status(thm)],[t102,t12]) ).
cnf(t104,plain,
true = ifeq(p_9(a,X1),true,ifeq(p_10(X1,a),true,false,true),true),
inference(step,[status(thm)],[t103,t12]) ).
cnf(t78,plain,
ifeq(p_9(a,X1),true,ifeq(p_10(X1,a),true,false,true),true) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(f9,negated_conjecture,
p_9(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_9) ).
fof(f9_nnf,plain,
p_9(a,a),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
p_9(a,a),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t9,plain,
p_9(a,a) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t30,plain,
p_9(a,a) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t79,plain,
true = ifeq(true,true,ifeq(p_10(a,a),true,false,true),true),
inference(cp,[status(thm)],[t78,t30]) ).
cnf(t105,plain,
true = ifeq(p_10(a,a),true,false,true),
inference(step,[status(thm)],[t79,t12]) ).
cnf(f10,negated_conjecture,
p_10(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_10) ).
fof(f10_nnf,plain,
p_10(a,a),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
p_10(a,a),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t1,plain,
p_10(a,a) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t28,plain,
p_10(a,a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t106,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t105,t28]) ).
cnf(t107,plain,
true = false,
inference(step,[status(thm)],[t106,t12]) ).
cnf(t86,plain,
false = true,
inference(orient,[status(thm)],[t107]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t86]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN005-1.010 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 23:54:42 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.58/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.58/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------