%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT259-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:56:27 PM UTC 2026
% Result : Unsatisfiable 5.36s 1.18s
% Output : Proof 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 44 unt; 0 def)
% Number of atoms : 68 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 42 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( V_U = V_V
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Oantisym(V_r,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_0) ).
fof(f3_nnf,plain,
! [V_r,T_a,V_V,V_U] :
( V_U = V_V
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Oantisym(V_r,T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_r,T_a,V_V,V_U] :
( V_U = V_V
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Oantisym(V_r,T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X3 = X2
| ~ c_in(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Relation_Oantisym(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
ifeq(c_Relation_Oantisym(X1,X2),true,ifeq(c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),true,ifeq(c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),true,X4,X3),X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t8,plain,
ifeq(c_Relation_Oantisym(X1,X2),true,ifeq(c_in(c_Pair(X3,X4,X2,X2),X1,tc_prod(X2,X2)),true,ifeq(c_in(c_Pair(X4,X3,X2,X2),X1,tc_prod(X2,X2)),true,X4,X3),X3),X3) = X3,
inference(orient,[status(thm)],[t6]) ).
cnf(f1,negated_conjecture,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t4,plain,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t13,plain,
v_b = ifeq(c_Relation_Oantisym(v_r,t_a),true,ifeq(true,true,ifeq(c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),true,v_a,v_b),v_b),v_b),
inference(cp,[status(thm)],[t8,t12]) ).
cnf(f4,axiom,
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
fof(f4_nnf,plain,
! [V_P,T_a] :
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_P,T_a] :
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X0,X1,tc_Product__Type_Ounit),X1)
| ~ c_in(X0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t16,plain,
ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),X2),true) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f6,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
fof(f6_nnf,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t0,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t18,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(orient,[status(thm)],[t0]) ).
cnf(t19,plain,
true = ifeq(c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,c_Relation_Oantisym(v_r,t_a),true),
inference(cp,[status(thm)],[t16,t18]) ).
cnf(f5,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
fof(f5_nnf,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t2,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t15,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t25,plain,
true = ifeq(true,true,c_Relation_Oantisym(v_r,t_a),true),
inference(step,[status(thm)],[t19,t15]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t26,plain,
true = c_Relation_Oantisym(v_r,t_a),
inference(step,[status(thm)],[t25,t7]) ).
cnf(t20,plain,
c_Relation_Oantisym(v_r,t_a) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(t27,plain,
v_b = ifeq(true,true,ifeq(true,true,ifeq(c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),true,v_a,v_b),v_b),v_b),
inference(step,[status(thm)],[t13,t20]) ).
cnf(t28,plain,
v_b = ifeq(true,true,ifeq(c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),true,v_a,v_b),v_b),
inference(step,[status(thm)],[t27,t7]) ).
cnf(t29,plain,
v_b = ifeq(c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),true,v_a,v_b),
inference(step,[status(thm)],[t28,t7]) ).
cnf(f0,negated_conjecture,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t3,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t9,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t30,plain,
v_b = ifeq(true,true,v_a,v_b),
inference(step,[status(thm)],[t29,t9]) ).
cnf(t31,plain,
v_b = v_a,
inference(step,[status(thm)],[t30,t7]) ).
cnf(t22,plain,
v_a = v_b,
inference(orient,[status(thm)],[t31]) ).
cnf(f2,negated_conjecture,
v_a != v_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
v_a != v_b,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
v_a != v_b,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
v_a != v_b,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
v_b != v_a,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
v_b != v_b,
inference(rw,[status(thm)],[goal_0,t22]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT259-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 20:48:50 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.36/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.36/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------