%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN061-1 : TPTP v9.3.1. Released v1.0.0.
% 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 03:33:39 PM UTC 2026
% Result : Unsatisfiable 5.16s 1.27s
% Output : Proof 5.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 42 unt; 0 def)
% Number of atoms : 74 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 32 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,negated_conjecture,
( ~ big_j(X)
| ~ big_i(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f5_nnf,plain,
! [X] :
( ~ big_j(X)
| ~ big_i(X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( ~ big_j(X)
| ~ big_i(X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ big_j(X0)
| ~ big_i(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t16,plain,
ifeq(big_i(X1),true,ifeq(big_j(X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t29,plain,
ifeq(big_i(X1),true,ifeq(big_j(X1),true,false,true),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f4,axiom,
( big_j(X)
| big_h(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f4_nnf,plain,
! [X] :
( big_j(X)
| big_h(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( big_j(X)
| big_h(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( big_j(X0)
| big_h(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t9,plain,
or(big_h(X1),big_j(X1)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t26,plain,
or(big_h(X1),big_j(X1)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t39,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(f1,axiom,
( ~ big_h(X)
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f1_nnf,plain,
! [X] :
( ~ big_h(X)
| ~ big_f(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ~ big_h(X)
| ~ big_f(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ big_h(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t12,plain,
or(not(big_f(X1)),not(big_h(X1))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t23,plain,
or(not(big_f(X1)),not(big_h(X1))) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(f3,axiom,
big_f(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f3_nnf,plain,
big_f(a),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
big_f(a),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t0,plain,
big_f(a) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t30,plain,
big_f(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,plain,
true = or(not(true),not(big_h(a))),
inference(cp,[status(thm)],[t23,t30]) ).
cnf(t3,plain,
not(true) = false,
introduced(definition) ).
cnf(t38,plain,
not(true) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t61,plain,
true = or(false,not(big_h(a))),
inference(step,[status(thm)],[t31,t38]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t18,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t62,plain,
true = not(big_h(a)),
inference(step,[status(thm)],[t61,t18]) ).
cnf(t42,plain,
not(big_h(a)) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t43,plain,
false = ifeq(true,true,big_h(a),false),
inference(cp,[status(thm)],[t39,t42]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t63,plain,
false = big_h(a),
inference(step,[status(thm)],[t43,t19]) ).
cnf(t44,plain,
big_h(a) = false,
inference(orient,[status(thm)],[t63]) ).
cnf(t45,plain,
true = or(false,big_j(a)),
inference(cp,[status(thm)],[t26,t44]) ).
cnf(t64,plain,
true = big_j(a),
inference(step,[status(thm)],[t45,t18]) ).
cnf(t47,plain,
big_j(a) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t48,plain,
true = ifeq(big_i(a),true,ifeq(true,true,false,true),true),
inference(cp,[status(thm)],[t29,t47]) ).
cnf(f2,axiom,
big_i(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f2_nnf,plain,
big_i(a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
big_i(a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t1,plain,
big_i(a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t35,plain,
big_i(a) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t65,plain,
true = ifeq(true,true,ifeq(true,true,false,true),true),
inference(step,[status(thm)],[t48,t35]) ).
cnf(t66,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t65,t19]) ).
cnf(t67,plain,
true = false,
inference(step,[status(thm)],[t66,t19]) ).
cnf(t50,plain,
false = true,
inference(orient,[status(thm)],[t67]) ).
cnf(f0,axiom,
( ~ big_g(X)
| ~ big_f(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f0_nnf,plain,
! [X] :
( ~ big_g(X)
| ~ big_f(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ~ big_g(X)
| ~ big_f(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ big_g(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t50]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 00:03:56 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.16/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/1.27 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------