%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN099-1.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:33:48 PM UTC 2026
% Result : Unsatisfiable 3.82s 0.99s
% Output : Proof 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 72 unt; 0 def)
% Number of atoms : 108 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 54 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 6 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( ~ p_1_2(X)
| ~ p_2_3(X)
| p_1_3(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s2_type11_3) ).
fof(f3_nnf,plain,
! [X] :
( ~ p_1_2(X)
| ~ p_2_3(X)
| p_1_3(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( ~ p_1_2(X)
| ~ p_2_3(X)
| p_1_3(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ p_1_2(X0)
| ~ p_2_3(X0)
| p_1_3(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t51,plain,
ifeq(p_2_3(X1),true,ifeq(p_1_2(X1),true,p_1_3(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f0,negated_conjecture,
~ p_1_3(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s2_goal_1) ).
fof(f0_nnf,plain,
! [X] : ~ p_1_3(X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ p_1_3(X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ p_1_3(X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
p_1_3(X1) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t63,plain,
p_1_3(X1) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t198,plain,
ifeq(p_2_3(X1),true,ifeq(p_1_2(X1),true,false,true),true) = true,
inference(step,[status(thm)],[t51,t63]) ).
cnf(t138,plain,
ifeq(p_2_3(X1),true,ifeq(p_1_2(X1),true,false,true),true) = true,
inference(orient,[status(thm)],[t198]) ).
cnf(f5,axiom,
( ~ p_2_2(X)
| ~ p_3_3(X)
| p_2_3(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s2_type11_5) ).
fof(f5_nnf,plain,
! [X] :
( ~ p_2_2(X)
| ~ p_3_3(X)
| p_2_3(X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( ~ p_2_2(X)
| ~ p_3_3(X)
| p_2_3(X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ p_2_2(X0)
| ~ p_3_3(X0)
| p_2_3(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t53,plain,
ifeq(p_3_3(X1),true,ifeq(p_2_2(X1),true,p_2_3(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t144,plain,
ifeq(p_3_3(X1),true,ifeq(p_2_2(X1),true,p_2_3(X1),true),true) = true,
inference(orient,[status(thm)],[t53]) ).
cnf(f21,axiom,
p_2_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t2_3) ).
fof(f21_nnf,plain,
p_2_2(a),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
p_2_2(a),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(t2,plain,
p_2_2(a) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t64,plain,
p_2_2(a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t145,plain,
true = ifeq(p_3_3(a),true,ifeq(true,true,p_2_3(a),true),true),
inference(cp,[status(thm)],[t144,t64]) ).
cnf(f23,axiom,
p_3_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t2_5) ).
fof(f23_nnf,plain,
p_3_3(a),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
p_3_3(a),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(t3,plain,
p_3_3(a) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t65,plain,
p_3_3(a) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t201,plain,
true = ifeq(true,true,ifeq(true,true,p_2_3(a),true),true),
inference(step,[status(thm)],[t145,t65]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t79,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t202,plain,
true = ifeq(true,true,p_2_3(a),true),
inference(step,[status(thm)],[t201,t79]) ).
cnf(t203,plain,
true = p_2_3(a),
inference(step,[status(thm)],[t202,t79]) ).
cnf(t146,plain,
p_2_3(a) = true,
inference(orient,[status(thm)],[t203]) ).
cnf(t150,plain,
true = ifeq(true,true,ifeq(p_1_2(a),true,false,true),true),
inference(cp,[status(thm)],[t138,t146]) ).
cnf(t204,plain,
true = ifeq(p_1_2(a),true,false,true),
inference(step,[status(thm)],[t150,t79]) ).
cnf(f1,axiom,
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_s2_type11_1) ).
fof(f1_nnf,plain,
! [X] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ~ p_1_1(X)
| ~ p_2_2(X)
| p_1_2(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ p_1_1(X0)
| ~ p_2_2(X0)
| p_1_2(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t49,plain,
ifeq(p_2_2(X1),true,ifeq(p_1_1(X1),true,p_1_2(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t130,plain,
ifeq(p_2_2(X1),true,ifeq(p_1_1(X1),true,p_1_2(X1),true),true) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(f19,axiom,
p_1_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_t2_1) ).
fof(f19_nnf,plain,
p_1_1(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
p_1_1(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(t0,plain,
p_1_1(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t62,plain,
p_1_1(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t131,plain,
true = ifeq(p_2_2(a),true,ifeq(true,true,p_1_2(a),true),true),
inference(cp,[status(thm)],[t130,t62]) ).
cnf(t192,plain,
true = ifeq(true,true,ifeq(true,true,p_1_2(a),true),true),
inference(step,[status(thm)],[t131,t64]) ).
cnf(t193,plain,
true = ifeq(true,true,p_1_2(a),true),
inference(step,[status(thm)],[t192,t79]) ).
cnf(t194,plain,
true = p_1_2(a),
inference(step,[status(thm)],[t193,t79]) ).
cnf(t132,plain,
p_1_2(a) = true,
inference(orient,[status(thm)],[t194]) ).
cnf(t205,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t204,t132]) ).
cnf(t206,plain,
true = false,
inference(step,[status(thm)],[t205,t79]) ).
cnf(t152,plain,
false = true,
inference(orient,[status(thm)],[t206]) ).
cnf(f44,axiom,
~ sym_p_1_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_1) ).
fof(f44_nnf,plain,
~ sym_p_1_1(a),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
~ sym_p_1_1(a),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
~ sym_p_1_1(a),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(f45,axiom,
~ sym_q_1_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_2) ).
fof(f45_nnf,plain,
~ sym_q_1_1(a),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
~ sym_q_1_1(a),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
~ sym_q_1_1(a),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(f46,axiom,
~ sym_p_2_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_3) ).
fof(f46_nnf,plain,
~ sym_p_2_2(a),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
~ sym_p_2_2(a),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
~ sym_p_2_2(a),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(f47,axiom,
~ sym_q_2_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_4) ).
fof(f47_nnf,plain,
~ sym_q_2_2(a),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
~ sym_q_2_2(a),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c47,plain,
~ sym_q_2_2(a),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(f48,axiom,
~ sym_p_3_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_5) ).
fof(f48_nnf,plain,
~ sym_p_3_3(a),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
~ sym_p_3_3(a),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
~ sym_p_3_3(a),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(f49,axiom,
~ sym_q_3_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym_m_t2_6) ).
fof(f49_nnf,plain,
~ sym_q_3_3(a),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
~ sym_q_3_3(a),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c49,plain,
~ sym_q_3_3(a),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c44,c45,c46,c47,c48,c49]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t152]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN099-1.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.38 % Computer : n019.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Fri Sep 25 00:10:05 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.82/0.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.82/0.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------