%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:42:18 PM UTC 2026
% Result : Unsatisfiable 7.81s 11.57s
% Output : Proof 7.81s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t158,axiom,
sF2 = ifeq(member(x,universal_class),true,false,true),
introduced(definition) ).
cnf(f148,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
fof(f148_nnf,plain,
~ member(x,universal_class),
inference(nnf_transformation,[status(thm)],[f148]) ).
fof(f148_sk,plain,
~ member(x,universal_class),
inference(skolemisation,[status(esa)],[f148_nnf]) ).
cnf(c148,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(esa)],[f148_sk]) ).
cnf(t8,plain,
member(x,universal_class) = false,
inference(equality_encoding,[status(esa)],[c148]) ).
cnf(t176,plain,
member(x,universal_class) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t156,axiom,
sF0 = member(x,universal_class),
introduced(definition) ).
cnf(t2066,plain,
sF0 = false,
inference(step,[status(thm)],[t156,t176]) ).
cnf(t185,plain,
false = sF0,
inference(orient,[status(thm)],[t2066]) ).
cnf(t2072,plain,
member(x,universal_class) = sF0,
inference(step,[status(thm)],[t176,t185]) ).
cnf(t191,plain,
member(x,universal_class) = sF0,
inference(orient,[status(thm)],[t2072]) ).
cnf(t2093,plain,
sF2 = ifeq(sF0,true,false,true),
inference(step,[status(thm)],[t158,t191]) ).
cnf(t2094,plain,
sF2 = ifeq(sF0,true,sF0,true),
inference(step,[status(thm)],[t2093,t185]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(t29,plain,
ifeq(member(X1,null_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t5,plain,
member(X1,null_class) = false,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t173,plain,
member(X1,null_class) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t2070,plain,
member(X1,null_class) = sF0,
inference(step,[status(thm)],[t173,t185]) ).
cnf(t189,plain,
member(X1,null_class) = sF0,
inference(orient,[status(thm)],[t2070]) ).
cnf(t2088,plain,
ifeq(sF0,true,false,true) = true,
inference(step,[status(thm)],[t29,t189]) ).
cnf(t2089,plain,
ifeq(sF0,true,sF0,true) = true,
inference(step,[status(thm)],[t2088,t185]) ).
cnf(t249,plain,
ifeq(sF0,true,sF0,true) = true,
inference(orient,[status(thm)],[t2089]) ).
cnf(t2095,plain,
sF2 = true,
inference(step,[status(thm)],[t2094,t249]) ).
cnf(t321,plain,
true = sF2,
inference(orient,[status(thm)],[t2095]) ).
cnf(f147,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
fof(f147_nnf,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(nnf_transformation,[status(thm)],[f147]) ).
fof(f147_sk,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(skolemisation,[status(esa)],[f147_nnf]) ).
cnf(c147,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(cnf_transformation,[status(esa)],[f147_sk]) ).
cnf(u41,axiom,
eq(unordered_pair(null_class,singleton(null_class)),ordered_pair(x,y)) = false,
inference(equality_encoding,[status(esa)],[c147]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(d0,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f12,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f12_nnf,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(u0,axiom,
unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(d1,axiom,
unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = ordered_pair(X0,X1),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t94,plain,
eq(unordered_pair(null_class,unordered_pair(null_class,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(definition_unfolding,[status(thm)],[u41,d0,d1]) ).
cnf(t28,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t248,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t2136,plain,
ifeq(eq(X1,X2),sF2,X1,X2) = X2,
inference(step,[status(thm)],[t248,t321]) ).
cnf(t369,plain,
ifeq(eq(X1,X2),sF2,X1,X2) = X2,
inference(rw,[status(thm)],[t2136]) ).
cnf(t468,plain,
ifeq(eq(X1,X2),sF2,X1,X2) = X2,
inference(orient,[status(thm)],[t369]) ).
cnf(f125,axiom,
( singleton(X) = null_class
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f125_nnf,plain,
! [X] :
( singleton(X) = null_class
| member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f125]) ).
fof(f125_sk,plain,
! [X] :
( singleton(X) = null_class
| member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f125_nnf]) ).
cnf(c125,plain,
( singleton(X0) = null_class
| member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f125_sk]) ).
cnf(u17,axiom,
or(member(X0,universal_class),eq(singleton(X0),null_class)) = true,
inference(equality_encoding,[status(esa)],[c125]) ).
cnf(t51,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = true,
inference(definition_unfolding,[status(thm)],[u17,d0]) ).
cnf(t2215,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = sF2,
inference(step,[status(thm)],[t51,t321]) ).
cnf(t532,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X1),null_class)) = sF2,
inference(orient,[status(thm)],[t2215]) ).
cnf(t533,plain,
sF2 = or(sF0,eq(unordered_pair(x,x),null_class)),
inference(cp,[status(thm)],[t532,t191]) ).
cnf(t12,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t180,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t2077,plain,
or(sF0,X1) = X1,
inference(step,[status(thm)],[t180,t185]) ).
cnf(t196,plain,
or(sF0,X1) = X1,
inference(rw,[status(thm)],[t2077]) ).
cnf(t204,plain,
or(sF0,X1) = X1,
inference(orient,[status(thm)],[t196]) ).
cnf(t2216,plain,
sF2 = eq(unordered_pair(x,x),null_class),
inference(step,[status(thm)],[t533,t204]) ).
cnf(t162,axiom,
sF6 = unordered_pair(x,x),
introduced(definition) ).
cnf(t201,plain,
unordered_pair(x,x) = sF6,
inference(orient,[status(thm)],[t162]) ).
cnf(t2217,plain,
sF2 = eq(sF6,null_class),
inference(step,[status(thm)],[t2216,t201]) ).
cnf(t535,plain,
eq(sF6,null_class) = sF2,
inference(orient,[status(thm)],[t2217]) ).
cnf(t536,plain,
null_class = ifeq(sF2,sF2,sF6,null_class),
inference(cp,[status(thm)],[t468,t535]) ).
cnf(t17,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t200,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t17]) ).
cnf(t2218,plain,
null_class = sF6,
inference(step,[status(thm)],[t536,t200]) ).
cnf(t537,plain,
null_class = sF6,
inference(orient,[status(thm)],[t2218]) ).
cnf(t2592,plain,
eq(unordered_pair(sF6,unordered_pair(null_class,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t94,t537]) ).
cnf(f111,axiom,
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f111_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f111]) ).
fof(f111_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) = singleton(Y)
| member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f111_nnf]) ).
cnf(c111,plain,
( unordered_pair(X0,X1) = singleton(X1)
| member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f111_sk]) ).
cnf(u11,axiom,
or(member(X0,universal_class),eq(unordered_pair(X0,X1),singleton(X1))) = true,
inference(equality_encoding,[status(esa)],[c111]) ).
cnf(t71,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = true,
inference(definition_unfolding,[status(thm)],[u11,d0]) ).
cnf(t2399,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = sF2,
inference(step,[status(thm)],[t71,t321]) ).
cnf(t1097,plain,
or(member(X1,universal_class),eq(unordered_pair(X1,X2),unordered_pair(X2,X2))) = sF2,
inference(orient,[status(thm)],[t2399]) ).
cnf(t1098,plain,
sF2 = or(sF0,eq(unordered_pair(x,X1),unordered_pair(X1,X1))),
inference(cp,[status(thm)],[t1097,t191]) ).
cnf(t2400,plain,
sF2 = eq(unordered_pair(x,X1),unordered_pair(X1,X1)),
inference(step,[status(thm)],[t1098,t204]) ).
cnf(t1104,plain,
eq(unordered_pair(x,X1),unordered_pair(X1,X1)) = sF2,
inference(orient,[status(thm)],[t2400]) ).
cnf(t1108,plain,
unordered_pair(X1,X1) = ifeq(sF2,sF2,unordered_pair(x,X1),unordered_pair(X1,X1)),
inference(cp,[status(thm)],[t468,t1104]) ).
cnf(t2456,plain,
unordered_pair(X1,X1) = unordered_pair(x,X1),
inference(step,[status(thm)],[t1108,t200]) ).
cnf(t1269,plain,
unordered_pair(X1,X1) = unordered_pair(x,X1),
inference(orient,[status(thm)],[t2456]) ).
cnf(t2593,plain,
eq(unordered_pair(sF6,unordered_pair(x,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2592,t1269]) ).
cnf(f149,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
fof(f149_nnf,plain,
~ member(y,universal_class),
inference(nnf_transformation,[status(thm)],[f149]) ).
fof(f149_sk,plain,
~ member(y,universal_class),
inference(skolemisation,[status(esa)],[f149_nnf]) ).
cnf(c149,plain,
~ member(y,universal_class),
inference(cnf_transformation,[status(esa)],[f149_sk]) ).
cnf(t9,plain,
member(y,universal_class) = false,
inference(equality_encoding,[status(esa)],[c149]) ).
cnf(t177,plain,
member(y,universal_class) = false,
inference(orient,[status(thm)],[t9]) ).
cnf(t2074,plain,
member(y,universal_class) = sF0,
inference(step,[status(thm)],[t177,t185]) ).
cnf(t193,plain,
member(y,universal_class) = sF0,
inference(orient,[status(thm)],[t2074]) ).
cnf(t1099,plain,
sF2 = or(sF0,eq(unordered_pair(y,X1),unordered_pair(X1,X1))),
inference(cp,[status(thm)],[t1097,t193]) ).
cnf(t2513,plain,
sF2 = eq(unordered_pair(y,X1),unordered_pair(X1,X1)),
inference(step,[status(thm)],[t1099,t204]) ).
cnf(t1511,plain,
eq(unordered_pair(y,X1),unordered_pair(X1,X1)) = sF2,
inference(orient,[status(thm)],[t2513]) ).
cnf(t1517,plain,
unordered_pair(X1,X1) = ifeq(sF2,sF2,unordered_pair(y,X1),unordered_pair(X1,X1)),
inference(cp,[status(thm)],[t468,t1511]) ).
cnf(t2518,plain,
unordered_pair(X1,X1) = unordered_pair(y,X1),
inference(step,[status(thm)],[t1517,t200]) ).
cnf(t1536,plain,
unordered_pair(X1,X1) = unordered_pair(y,X1),
inference(orient,[status(thm)],[t2518]) ).
cnf(t1540,plain,
unordered_pair(y,X1) = unordered_pair(x,X1),
inference(cp,[status(thm)],[t1536,t1269]) ).
cnf(t1566,plain,
unordered_pair(x,X1) = unordered_pair(y,X1),
inference(orient,[status(thm)],[t1540]) ).
cnf(t2594,plain,
eq(unordered_pair(sF6,unordered_pair(y,null_class)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2593,t1566]) ).
cnf(t2595,plain,
eq(unordered_pair(sF6,unordered_pair(y,sF6)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2594,t537]) ).
cnf(f107,axiom,
unordered_pair(X,Y) = unordered_pair(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f107_nnf,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(nnf_transformation,[status(thm)],[f107]) ).
fof(f107_sk,plain,
! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
inference(skolemisation,[status(esa)],[f107_nnf]) ).
cnf(c107,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
cnf(t23,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t223,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(orient,[status(thm)],[t23]) ).
cnf(t2596,plain,
eq(unordered_pair(sF6,unordered_pair(sF6,y)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2595,t223]) ).
cnf(t1538,plain,
unordered_pair(y,X1) = unordered_pair(X1,X1),
inference(cp,[status(thm)],[t1536,t223]) ).
cnf(t1593,plain,
unordered_pair(y,X1) = unordered_pair(X1,X1),
inference(orient,[status(thm)],[t1538]) ).
cnf(t1594,plain,
unordered_pair(X1,X1) = unordered_pair(X1,y),
inference(cp,[status(thm)],[t1593,t223]) ).
cnf(t1667,plain,
unordered_pair(X1,X1) = unordered_pair(X1,y),
inference(orient,[status(thm)],[t1594]) ).
cnf(t2597,plain,
eq(unordered_pair(sF6,unordered_pair(sF6,sF6)),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2596,t1667]) ).
cnf(t160,axiom,
sF4 = unordered_pair(null_class,null_class),
introduced(definition) ).
cnf(t199,plain,
unordered_pair(null_class,null_class) = sF4,
inference(orient,[status(thm)],[t160]) ).
cnf(t2221,plain,
unordered_pair(sF6,null_class) = sF4,
inference(step,[status(thm)],[t199,t537]) ).
cnf(t2222,plain,
unordered_pair(sF6,sF6) = sF4,
inference(step,[status(thm)],[t2221,t537]) ).
cnf(t541,plain,
unordered_pair(sF6,sF6) = sF4,
inference(rw,[status(thm)],[t2222]) ).
cnf(t570,plain,
unordered_pair(sF6,sF6) = sF4,
inference(orient,[status(thm)],[t541]) ).
cnf(t2598,plain,
eq(unordered_pair(sF6,sF4),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2597,t570]) ).
cnf(t2599,plain,
eq(unordered_pair(sF4,sF6),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2598,t223]) ).
cnf(t161,axiom,
sF5 = unordered_pair(null_class,unordered_pair(null_class,null_class)),
introduced(definition) ).
cnf(t2081,plain,
sF5 = unordered_pair(null_class,sF4),
inference(step,[status(thm)],[t161,t199]) ).
cnf(t217,plain,
unordered_pair(null_class,sF4) = sF5,
inference(orient,[status(thm)],[t2081]) ).
cnf(t2083,plain,
unordered_pair(sF4,null_class) = sF5,
inference(step,[status(thm)],[t217,t223]) ).
cnf(t224,plain,
unordered_pair(sF4,null_class) = sF5,
inference(rw,[status(thm)],[t2083]) ).
cnf(t226,plain,
unordered_pair(sF4,null_class) = sF5,
inference(orient,[status(thm)],[t224]) ).
cnf(t2224,plain,
unordered_pair(sF4,sF6) = sF5,
inference(step,[status(thm)],[t226,t537]) ).
cnf(t543,plain,
unordered_pair(sF4,sF6) = sF5,
inference(rw,[status(thm)],[t2224]) ).
cnf(t573,plain,
unordered_pair(sF4,sF6) = sF5,
inference(orient,[status(thm)],[t543]) ).
cnf(t2600,plain,
eq(sF5,unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2599,t573]) ).
cnf(t2601,plain,
eq(sF5,unordered_pair(unordered_pair(y,x),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2600,t1566]) ).
cnf(t1274,plain,
unordered_pair(x,X1) = unordered_pair(X1,X1),
inference(cp,[status(thm)],[t1269,t223]) ).
cnf(t1423,plain,
unordered_pair(x,X1) = unordered_pair(X1,X1),
inference(orient,[status(thm)],[t1274]) ).
cnf(t1424,plain,
unordered_pair(X1,X1) = unordered_pair(X1,x),
inference(cp,[status(thm)],[t1423,t223]) ).
cnf(t1433,plain,
unordered_pair(X1,X1) = unordered_pair(X1,x),
inference(orient,[status(thm)],[t1424]) ).
cnf(t1541,plain,
unordered_pair(y,X1) = unordered_pair(X1,x),
inference(cp,[status(thm)],[t1536,t1433]) ).
cnf(t1626,plain,
unordered_pair(y,X1) = unordered_pair(X1,x),
inference(orient,[status(thm)],[t1541]) ).
cnf(t1628,plain,
unordered_pair(X1,x) = unordered_pair(X1,y),
inference(cp,[status(thm)],[t1626,t223]) ).
cnf(t1641,plain,
unordered_pair(X1,x) = unordered_pair(X1,y),
inference(orient,[status(thm)],[t1628]) ).
cnf(t2602,plain,
eq(sF5,unordered_pair(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2601,t1641]) ).
cnf(t163,axiom,
sF7 = unordered_pair(y,y),
introduced(definition) ).
cnf(t202,plain,
unordered_pair(y,y) = sF7,
inference(orient,[status(thm)],[t163]) ).
cnf(t1105,plain,
sF2 = eq(unordered_pair(x,y),sF7),
inference(cp,[status(thm)],[t1104,t202]) ).
cnf(t2401,plain,
sF2 = eq(unordered_pair(y,x),sF7),
inference(step,[status(thm)],[t1105,t223]) ).
cnf(t1109,plain,
eq(unordered_pair(y,x),sF7) = sF2,
inference(orient,[status(thm)],[t2401]) ).
cnf(t1111,plain,
sF7 = ifeq(sF2,sF2,unordered_pair(y,x),sF7),
inference(cp,[status(thm)],[t468,t1109]) ).
cnf(t2402,plain,
sF7 = unordered_pair(y,x),
inference(step,[status(thm)],[t1111,t200]) ).
cnf(t1112,plain,
unordered_pair(y,x) = sF7,
inference(orient,[status(thm)],[t2402]) ).
cnf(t1117,plain,
sF2 = or(member(y,universal_class),eq(sF7,unordered_pair(x,x))),
inference(cp,[status(thm)],[t1097,t1112]) ).
cnf(t2403,plain,
sF2 = or(sF0,eq(sF7,unordered_pair(x,x))),
inference(step,[status(thm)],[t1117,t193]) ).
cnf(t2404,plain,
sF2 = eq(sF7,unordered_pair(x,x)),
inference(step,[status(thm)],[t2403,t204]) ).
cnf(t2405,plain,
sF2 = eq(sF7,sF6),
inference(step,[status(thm)],[t2404,t201]) ).
cnf(t1118,plain,
eq(sF7,sF6) = sF2,
inference(orient,[status(thm)],[t2405]) ).
cnf(t1119,plain,
sF6 = ifeq(sF2,sF2,sF7,sF6),
inference(cp,[status(thm)],[t468,t1118]) ).
cnf(t2406,plain,
sF6 = sF7,
inference(step,[status(thm)],[t1119,t200]) ).
cnf(t1120,plain,
sF7 = sF6,
inference(orient,[status(thm)],[t2406]) ).
cnf(t2407,plain,
unordered_pair(y,y) = sF6,
inference(step,[status(thm)],[t202,t1120]) ).
cnf(t1121,plain,
unordered_pair(y,y) = sF6,
inference(orient,[status(thm)],[t2407]) ).
cnf(t2603,plain,
eq(sF5,unordered_pair(sF6,unordered_pair(x,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2602,t1121]) ).
cnf(t2604,plain,
eq(sF5,unordered_pair(sF6,unordered_pair(y,unordered_pair(y,y)))) = false,
inference(step,[status(thm)],[t2603,t1566]) ).
cnf(t2605,plain,
eq(sF5,unordered_pair(sF6,unordered_pair(y,sF6))) = false,
inference(step,[status(thm)],[t2604,t1121]) ).
cnf(t2606,plain,
eq(sF5,unordered_pair(sF6,unordered_pair(sF6,y))) = false,
inference(step,[status(thm)],[t2605,t223]) ).
cnf(t2607,plain,
eq(sF5,unordered_pair(sF6,unordered_pair(sF6,sF6))) = false,
inference(step,[status(thm)],[t2606,t1667]) ).
cnf(t2608,plain,
eq(sF5,unordered_pair(sF6,sF4)) = false,
inference(step,[status(thm)],[t2607,t570]) ).
cnf(t2609,plain,
eq(sF5,unordered_pair(sF4,sF6)) = false,
inference(step,[status(thm)],[t2608,t223]) ).
cnf(t2610,plain,
eq(sF5,sF5) = false,
inference(step,[status(thm)],[t2609,t573]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t172,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t2101,plain,
eq(X1,X1) = sF2,
inference(step,[status(thm)],[t172,t321]) ).
cnf(t327,plain,
eq(X1,X1) = sF2,
inference(orient,[status(thm)],[t2101]) ).
cnf(t2611,plain,
sF2 = false,
inference(step,[status(thm)],[t2610,t327]) ).
cnf(t2612,plain,
sF2 = sF0,
inference(step,[status(thm)],[t2611,t185]) ).
cnf(t1832,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t2612]) ).
cnf(t2649,plain,
true = sF0,
inference(step,[status(thm)],[t321,t1832]) ).
cnf(t1869,plain,
true = sF0,
inference(orient,[status(thm)],[t2649]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f101_nnf,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f115_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f116,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f116_nnf,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f117_nnf,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f122,axiom,
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f122_nnf,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c115,c116,c117,c122,c147,c148,c149]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t1869]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t185]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/10.38 % Computer : n018.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 09:53:14 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.81/11.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.81/11.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------