%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT277-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 01:56:35 PM UTC 2026
% Result : Unsatisfiable 5.92s 1.29s
% Output : Proof 5.92s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sFlat0 = c_Pair(v_x,v_x,t_a,t_a),
introduced(definition) ).
cnf(t32,plain,
c_Pair(v_x,v_x,t_a,t_a) = sFlat0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sFlat1 = tc_prod(t_a,t_a),
introduced(definition) ).
cnf(t24,plain,
tc_prod(t_a,t_a) = sFlat1,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sFlat2 = c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
introduced(definition) ).
cnf(t21,plain,
c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) = sFlat2,
inference(orient,[status(thm)],[t10]) ).
cnf(t51,plain,
c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,sFlat1) = sFlat2,
inference(step,[status(thm)],[t21,t24]) ).
cnf(t26,plain,
c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,sFlat1) = sFlat2,
inference(rw,[status(thm)],[t51]) ).
cnf(t56,plain,
c_in(sFlat0,v_r,sFlat1) = sFlat2,
inference(step,[status(thm)],[t26,t32]) ).
cnf(t36,plain,
c_in(sFlat0,v_r,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t56]) ).
cnf(f2,axiom,
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OreflD_0) ).
fof(f2_nnf,plain,
! [V_A,V_r,T_a,V_a] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_A,V_r,T_a,V_a] :
( c_in(c_Pair(V_a,V_a,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(V_a,V_A,T_a)
| ~ c_Relation_Orefl(V_A,V_r,T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(c_Pair(X3,X3,X2,X2),X1,tc_prod(X2,X2))
| ~ c_in(X3,X0,X2)
| ~ c_Relation_Orefl(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
ifeq(c_Relation_Orefl(X1,X2,X3),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t16,plain,
ifeq(c_Relation_Orefl(X1,X2,X3),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,X4,X3,X3),X2,tc_prod(X3,X3)),true),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f4,axiom,
( c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_0) ).
fof(f4_nnf,plain,
! [V_P,T_a] :
( c_Relation_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(V_P,T_a,tc_Product__Type_Ounit),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_Orefl(c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit),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(t6,plain,
ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,c_Relation_Orefl(c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t14,plain,
ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,c_Relation_Orefl(c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),X2),true) = true,
inference(orient,[status(thm)],[t6]) ).
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(t30,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,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_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_r,t_a),true),
inference(cp,[status(thm)],[t14,t30]) ).
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(t4,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(t12,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)],[t4]) ).
cnf(t53,plain,
true = ifeq(true,true,c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_r,t_a),true),
inference(step,[status(thm)],[t31,t12]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t54,plain,
true = c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_r,t_a),
inference(step,[status(thm)],[t53,t11]) ).
cnf(f3,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
fof(f3_nnf,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t1,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t27,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(orient,[status(thm)],[t1]) ).
cnf(t55,plain,
true = c_Relation_Orefl(v_A,v_r,t_a),
inference(step,[status(thm)],[t54,t27]) ).
cnf(t34,plain,
c_Relation_Orefl(v_A,v_r,t_a) = true,
inference(orient,[status(thm)],[t55]) ).
cnf(t35,plain,
true = ifeq(true,true,ifeq(c_in(X1,v_A,t_a),true,c_in(c_Pair(X1,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)),true),true),
inference(cp,[status(thm)],[t16,t34]) ).
cnf(t57,plain,
true = ifeq(c_in(X1,v_A,t_a),true,c_in(c_Pair(X1,X1,t_a,t_a),v_r,tc_prod(t_a,t_a)),true),
inference(step,[status(thm)],[t35,t11]) ).
cnf(t58,plain,
true = ifeq(c_in(X1,v_A,t_a),true,c_in(c_Pair(X1,X1,t_a,t_a),v_r,sFlat1),true),
inference(step,[status(thm)],[t57,t24]) ).
cnf(t38,plain,
ifeq(c_in(X1,v_A,t_a),true,c_in(c_Pair(X1,X1,t_a,t_a),v_r,sFlat1),true) = true,
inference(orient,[status(thm)],[t58]) ).
cnf(f0,negated_conjecture,
c_in(v_x,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_x,v_A,t_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_x,v_A,t_a),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(t2,plain,
c_in(v_x,v_A,t_a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
c_in(v_x,v_A,t_a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t39,plain,
true = ifeq(true,true,c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,sFlat1),true),
inference(cp,[status(thm)],[t38,t13]) ).
cnf(t59,plain,
true = c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,sFlat1),
inference(step,[status(thm)],[t39,t11]) ).
cnf(t60,plain,
true = c_in(sFlat0,v_r,sFlat1),
inference(step,[status(thm)],[t59,t32]) ).
cnf(t61,plain,
true = sFlat2,
inference(step,[status(thm)],[t60,t36]) ).
cnf(t41,plain,
true = sFlat2,
inference(orient,[status(thm)],[t61]) ).
cnf(f1,negated_conjecture,
~ c_in(c_Pair(v_x,v_x,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_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
c_in(sFlat0,v_r,tc_prod(t_a,t_a)) != true,
inference(rw,[status(thm)],[goal_0,t32]) ).
cnf(g0_1,plain,
c_in(sFlat0,v_r,sFlat1) != true,
inference(rw,[status(thm)],[g0_0,t24]) ).
cnf(g0_2,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_1,t36]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t41]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT277-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Wed Sep 23 20:48:03 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.92/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.92/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------