%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN035-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 03:33:21 PM UTC 2026
% Result : Unsatisfiable 3.25s 0.83s
% Output : Proof 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 59 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 68 ( 20 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B))
| ~ q(A,f(A,B))
| ~ q(f(A,B),f(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B))
| ~ q(A,f(A,B))
| ~ q(f(A,B),f(A,B)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B))
| ~ q(A,f(A,B))
| ~ q(f(A,B),f(A,B)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ p(X1,f(X0,X1))
| ~ p(f(X0,X1),f(X0,X1))
| ~ q(X0,f(X0,X1))
| ~ q(f(X0,X1),f(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,ifeq(p(f(X1,X2),f(X1,X2)),true,ifeq(p(X2,f(X1,X2)),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t6,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,ifeq(p(f(X1,X2),f(X1,X2)),true,ifeq(p(X2,f(X1,X2)),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f0,axiom,
p(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f0_nnf,plain,
! [A,B] : p(A,B),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : p(A,B),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p(X0,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
p(X1,X2) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
p(X1,X2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t16,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,ifeq(true,true,ifeq(p(X2,f(X1,X2)),true,false,true),true),true),true) = true,
inference(step,[status(thm)],[t6,t7]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t17,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,ifeq(p(X2,f(X1,X2)),true,false,true),true),true) = true,
inference(step,[status(thm)],[t16,t4]) ).
cnf(t18,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,ifeq(true,true,false,true),true),true) = true,
inference(step,[status(thm)],[t17,t7]) ).
cnf(t19,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,false,true),true) = true,
inference(step,[status(thm)],[t18,t4]) ).
cnf(t9,plain,
ifeq(q(f(X1,X2),f(X1,X2)),true,ifeq(q(X1,f(X1,X2)),true,false,true),true) = true,
inference(rw,[status(thm)],[t19]) ).
cnf(f1,axiom,
( q(A,B)
| ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
fof(f1_nnf,plain,
! [A,B] :
( q(A,B)
| ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( q(A,B)
| ~ p(B,f(A,B))
| ~ p(f(A,B),f(A,B)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( q(X0,X1)
| ~ p(X1,f(X0,X1))
| ~ p(f(X0,X1),f(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
ifeq(p(f(X1,X2),f(X1,X2)),true,ifeq(p(X2,f(X1,X2)),true,q(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t5,plain,
ifeq(p(f(X1,X2),f(X1,X2)),true,ifeq(p(X2,f(X1,X2)),true,q(X1,X2),true),true) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t12,plain,
ifeq(true,true,ifeq(p(X2,f(X1,X2)),true,q(X1,X2),true),true) = true,
inference(step,[status(thm)],[t5,t7]) ).
cnf(t13,plain,
ifeq(p(X2,f(X1,X2)),true,q(X1,X2),true) = true,
inference(step,[status(thm)],[t12,t4]) ).
cnf(t14,plain,
ifeq(true,true,q(X1,X2),true) = true,
inference(step,[status(thm)],[t13,t7]) ).
cnf(t15,plain,
q(X1,X2) = true,
inference(step,[status(thm)],[t14,t4]) ).
cnf(t8,plain,
q(X1,X2) = true,
inference(rw,[status(thm)],[t15]) ).
cnf(t10,plain,
q(X1,X2) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t20,plain,
ifeq(true,true,ifeq(q(X1,f(X1,X2)),true,false,true),true) = true,
inference(step,[status(thm)],[t9,t10]) ).
cnf(t21,plain,
ifeq(q(X1,f(X1,X2)),true,false,true) = true,
inference(step,[status(thm)],[t20,t4]) ).
cnf(t22,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t21,t10]) ).
cnf(t23,plain,
false = true,
inference(step,[status(thm)],[t22,t4]) ).
cnf(t11,plain,
false = true,
inference(orient,[status(thm)],[t23]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 23:51:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.25/0.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/0.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------