%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : CSR150^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Wed Sep 30 07:47:12 AM UTC 2026
% Result : Theorem 0.24s 0.38s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR150^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n006.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 17:57:09 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.38 % (1098707)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.38 % (1098712)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1660297887:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.38 % (1098712)Refutation not found, incomplete strategy
% 0.24/0.38 % (1098712)------------------------------
% 0.24/0.38 % (1098712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098712)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098712)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.38 % (1098712)Time elapsed: 0.002 s
% 0.24/0.38 % (1098712)Peak memory usage: 12 MB
% 0.24/0.38 % (1098712)Instructions burned: 2 (million)
% 0.24/0.38 % (1098712)------------------------------
% 0.24/0.38 % (1098712)------------------------------
% 0.24/0.38 % (1098718)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.38 % (1098718)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.38 % (1098718)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1925644962:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.38 % (1098713)lrs+10_16_si=on:nwc=1.5:random_seed=836463393:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.38 % (1098714)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1352192373:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.38 % (1098716)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3436059920:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.38 % (1098717)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3848193162:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.38 % (1098715)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3826389507:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.38 % (1098714)Refutation not found, incomplete strategy
% 0.24/0.38 % (1098714)------------------------------
% 0.24/0.38 % (1098714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098714)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098714)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.38 % (1098714)Time elapsed: 0.003 s
% 0.24/0.38 % (1098714)Peak memory usage: 12 MB
% 0.24/0.38 % (1098714)Instructions burned: 2 (million)
% 0.24/0.38 % (1098718)Refutation not found, incomplete strategy
% 0.24/0.38 % (1098718)------------------------------
% 0.24/0.38 % (1098718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098718)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098718)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.38 % (1098718)Time elapsed: 0.006 s
% 0.24/0.38 % (1098718)Peak memory usage: 12 MB
% 0.24/0.38 % (1098718)Instructions burned: 4 (million)
% 0.24/0.38 % (1098714)------------------------------
% 0.24/0.38 % (1098714)------------------------------
% 0.24/0.38 % (1098715)Refutation not found, incomplete strategy
% 0.24/0.38 % (1098715)------------------------------
% 0.24/0.38 % (1098715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098715)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098715)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.38 % (1098715)Time elapsed: 0.004 s
% 0.24/0.38 % (1098715)Peak memory usage: 12 MB
% 0.24/0.38 % (1098715)Instructions burned: 3 (million)
% 0.24/0.38 % (1098718)------------------------------
% 0.24/0.38 % (1098718)------------------------------
% 0.24/0.38 % (1098715)------------------------------
% 0.24/0.38 % (1098715)------------------------------
% 0.24/0.38 % (1098713) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1098707-1098713"...
% 0.24/0.38 % (1098720)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3001443573:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.38 % (1098713)...printing done.
% 0.24/0.38 % (1098720)Instruction limit reached!
% 0.24/0.38 % (1098720)------------------------------
% 0.24/0.38 % (1098720)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098720)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098720)Termination reason: Instruction limit
% 0.24/0.38 % (1098720)Termination phase: Saturation
% 0.24/0.38 % (1098720)Time elapsed: 0.002 s
% 0.24/0.38 % (1098720)Peak memory usage: 12 MB
% 0.24/0.38 % (1098720)Instructions burned: 2 (million)
% 0.24/0.38 % (1098713)Refutation found. Thanks to Tanya!
% 0.24/0.38 % SZS status Theorem for theBenchmark
% 0.24/0.38 % SZS output start Proof for theBenchmark
% 0.24/0.38 thf(type_def_5, type, num: $tType).
% 0.24/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.38 thf(func_def_0, type, grandchild_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.38 thf(func_def_1, type, grandparent_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.38 thf(func_def_2, type, lCardinalityFn_THFTYPE_IIioIiI: (($i > $o) > $i)).
% 0.24/0.38 thf(func_def_4, type, ltet_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.38 thf(func_def_6, type, parent_THFTYPE_IiioI: ($i > $i > $o)).
% 0.24/0.38 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.38 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.38 thf(func_def_12, type, sK0: ($i > $i > $i)).
% 0.24/0.38 thf(func_def_13, type, sK1: ($i > $i > $i)).
% 0.24/0.38 thf(f1,axiom,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : ((grandparent_THFTYPE_IiioI @ X0 @ X1) <=> ? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X1) & (parent_THFTYPE_IiioI @ X0 @ X2)))),
% 0.24/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax)).
% 0.24/0.38 thf(f2,axiom,(
% 0.24/0.38 (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)))) @ n3_THFTYPE_i)),
% 0.24/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_001)).
% 0.24/0.38 thf(f3,axiom,(
% 0.24/0.38 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X0) & (parent_THFTYPE_IiioI @ X1 @ X2)) <=> (grandchild_THFTYPE_IiioI @ X0 @ X1))),
% 0.24/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_002)).
% 0.24/0.38 thf(f4,conjecture,(
% 0.24/0.38 ? [X0 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X1 : $i] : ((grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i)))) @ X0)),
% 0.24/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.24/0.38 thf(f5,negated_conjecture,(
% 0.24/0.38 ~ ? [X0 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X1 : $i] : ((grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i)))) @ X0)),
% 0.24/0.38 inference(negated_conjecture,[status(cth)],[f4])).
% 0.24/0.38 thf(f6,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : ((grandparent_THFTYPE_IiioI @ X0 @ X1) <=> ? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X1) & (parent_THFTYPE_IiioI @ X0 @ X2)))),
% 0.24/0.38 inference(rectify,[],[f1])).
% 0.24/0.38 thf(f7,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : ((((grandparent_THFTYPE_IiioI @ X0 @ X1)) = $true) <=> ? [X2 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X2)) = $true) & (((parent_THFTYPE_IiioI @ X2 @ X1)) = $true)))),
% 0.24/0.38 inference(fool_elimination,[],[f6])).
% 0.24/0.38 thf(f8,plain,(
% 0.24/0.38 (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X0 : $i] : ((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X0)))) @ n3_THFTYPE_i)),
% 0.24/0.38 inference(rectify,[],[f2])).
% 0.24/0.38 thf(f9,plain,(
% 0.24/0.38 (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0))) @ n3_THFTYPE_i)) = $true)),
% 0.24/0.38 inference(fool_elimination,[],[f8])).
% 0.24/0.38 thf(f10,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((parent_THFTYPE_IiioI @ X2 @ X1) & (parent_THFTYPE_IiioI @ X0 @ X2)) <=> (grandchild_THFTYPE_IiioI @ X1 @ X0))),
% 0.24/0.38 inference(rectify,[],[f3])).
% 0.24/0.38 thf(f11,plain,(
% 0.24/0.38 ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((parent_THFTYPE_IiioI @ X2 @ X1)) = $true) & (((parent_THFTYPE_IiioI @ X0 @ X2)) = $true)) <=> (((grandchild_THFTYPE_IiioI @ X1 @ X0)) = $true))),
% 0.24/0.38 inference(fool_elimination,[],[f10])).
% 0.24/0.38 thf(f12,plain,(
% 0.24/0.38 ~ ? [X0 : $i] : (ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[X1 : $i] : ((grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i)))) @ X0)),
% 0.24/0.38 inference(rectify,[],[f5])).
% 0.24/0.38 thf(f13,plain,(
% 0.24/0.38 ~ ? [X0 : $i] : (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0)) = $true)),
% 0.24/0.38 inference(fool_elimination,[],[f12])).
% 0.24/0.38 thf(f14,plain,(
% 0.24/0.38 ! [X0 : $i] : (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0)) != $true)),
% 0.24/0.38 inference(ennf_transformation,[],[f13])).
% 0.24/0.38 thf(f15,plain,(
% 0.24/0.38 ! [X1 : $i,X0 : $i] : ((? [X2 : $i] : ((((parent_THFTYPE_IiioI @ X2 @ X1)) = $true) & (((parent_THFTYPE_IiioI @ X0 @ X2)) = $true)) | (((grandchild_THFTYPE_IiioI @ X1 @ X0)) != $true)) & ((((grandchild_THFTYPE_IiioI @ X1 @ X0)) = $true) | ! [X2 : $i] : ((((parent_THFTYPE_IiioI @ X2 @ X1)) != $true) | (((parent_THFTYPE_IiioI @ X0 @ X2)) != $true))))),
% 0.24/0.38 inference(nnf_transformation,[],[f11])).
% 0.24/0.38 thf(f16,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : ((? [X2 : $i] : ((((parent_THFTYPE_IiioI @ X2 @ X0)) = $true) & (((parent_THFTYPE_IiioI @ X1 @ X2)) = $true)) | (((grandchild_THFTYPE_IiioI @ X0 @ X1)) != $true)) & ((((grandchild_THFTYPE_IiioI @ X0 @ X1)) = $true) | ! [X3 : $i] : ((((parent_THFTYPE_IiioI @ X3 @ X0)) != $true) | (((parent_THFTYPE_IiioI @ X1 @ X3)) != $true))))),
% 0.24/0.38 inference(rectify,[],[f15])).
% 0.24/0.38 thf(f17,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : ((((((parent_THFTYPE_IiioI @ (sK0 @ X1 @ X0) @ X0)) = $true) & (((parent_THFTYPE_IiioI @ X1 @ (sK0 @ X1 @ X0))) = $true)) | (((grandchild_THFTYPE_IiioI @ X0 @ X1)) != $true)) & ((((grandchild_THFTYPE_IiioI @ X0 @ X1)) = $true) | ! [X3 : $i] : ((((parent_THFTYPE_IiioI @ X3 @ X0)) != $true) | (((parent_THFTYPE_IiioI @ X1 @ X3)) != $true))))),
% 0.24/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f16])).
% 0.24/0.38 thf(f18,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : (((((grandparent_THFTYPE_IiioI @ X0 @ X1)) = $true) | ! [X2 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X2)) != $true) | (((parent_THFTYPE_IiioI @ X2 @ X1)) != $true))) & (? [X2 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X2)) = $true) & (((parent_THFTYPE_IiioI @ X2 @ X1)) = $true)) | (((grandparent_THFTYPE_IiioI @ X0 @ X1)) != $true)))),
% 0.24/0.38 inference(nnf_transformation,[],[f7])).
% 0.24/0.38 thf(f19,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : (((((grandparent_THFTYPE_IiioI @ X0 @ X1)) = $true) | ! [X2 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X2)) != $true) | (((parent_THFTYPE_IiioI @ X2 @ X1)) != $true))) & (? [X3 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X3)) = $true) & (((parent_THFTYPE_IiioI @ X3 @ X1)) = $true)) | (((grandparent_THFTYPE_IiioI @ X0 @ X1)) != $true)))),
% 0.24/0.38 inference(rectify,[],[f18])).
% 0.24/0.38 thf(f20,plain,(
% 0.24/0.38 ! [X0 : $i,X1 : $i] : (((((grandparent_THFTYPE_IiioI @ X0 @ X1)) = $true) | ! [X2 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ X2)) != $true) | (((parent_THFTYPE_IiioI @ X2 @ X1)) != $true))) & (((((parent_THFTYPE_IiioI @ X0 @ (sK1 @ X1 @ X0))) = $true) & (((parent_THFTYPE_IiioI @ (sK1 @ X1 @ X0) @ X1)) = $true)) | (((grandparent_THFTYPE_IiioI @ X0 @ X1)) != $true)))),
% 0.24/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f19])).
% 0.24/0.38 thf(f21,plain,(
% 0.24/0.38 ( ! [X3 : $i,X0 : $i,X1 : $i] : ((((parent_THFTYPE_IiioI @ X3 @ X0)) != $true) | (((grandchild_THFTYPE_IiioI @ X0 @ X1)) = $true) | (((parent_THFTYPE_IiioI @ X1 @ X3)) != $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f17])).
% 0.24/0.38 thf(f22,plain,(
% 0.24/0.38 ( ! [X0 : $i,X1 : $i] : ((((grandchild_THFTYPE_IiioI @ X0 @ X1)) != $true) | (((parent_THFTYPE_IiioI @ X1 @ (sK0 @ X1 @ X0))) = $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f17])).
% 0.24/0.38 thf(f23,plain,(
% 0.24/0.38 ( ! [X0 : $i,X1 : $i] : ((((grandchild_THFTYPE_IiioI @ X0 @ X1)) != $true) | (((parent_THFTYPE_IiioI @ (sK0 @ X1 @ X0) @ X0)) = $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f17])).
% 0.24/0.38 thf(f24,plain,(
% 0.24/0.38 ( ! [X0 : $i] : ((((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) @ X0)) != $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f14])).
% 0.24/0.38 thf(f25,plain,(
% 0.24/0.38 (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (^[Y0 : $i]: (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Y0))) @ n3_THFTYPE_i)) = $true)),
% 0.24/0.38 inference(cnf_transformation,[],[f9])).
% 0.24/0.38 thf(f26,plain,(
% 0.24/0.38 ( ! [X0 : $i,X1 : $i] : ((((grandparent_THFTYPE_IiioI @ X0 @ X1)) != $true) | (((parent_THFTYPE_IiioI @ (sK1 @ X1 @ X0) @ X1)) = $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f20])).
% 0.24/0.38 thf(f27,plain,(
% 0.24/0.38 ( ! [X0 : $i,X1 : $i] : ((((grandparent_THFTYPE_IiioI @ X0 @ X1)) != $true) | (((parent_THFTYPE_IiioI @ X0 @ (sK1 @ X1 @ X0))) = $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f20])).
% 0.24/0.38 thf(f28,plain,(
% 0.24/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((parent_THFTYPE_IiioI @ X2 @ X1)) != $true) | (((grandparent_THFTYPE_IiioI @ X0 @ X1)) = $true) | (((parent_THFTYPE_IiioI @ X0 @ X2)) != $true)) )),
% 0.24/0.38 inference(cnf_transformation,[],[f20])).
% 0.24/0.38 thf(f31,plain,(
% 0.24/0.38 (((ltet_THFTYPE_IiioI @ (lCardinalityFn_THFTYPE_IIioIiI @ (grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i)) @ n3_THFTYPE_i)) = $true)),
% 0.24/0.38 inference(beta-eta_normalization,[],[f25])).
% 0.24/0.38 thf(f32,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i)) != (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i))) | ($true != $true)),
% 0.24/0.38 inference(constrained_superposition,[],[f24,f31])).
% 0.24/0.38 thf(f33,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i)) != (^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)))),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f32])).
% 0.24/0.38 thf(f34,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) != (((^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)) @ sK2)))),
% 0.24/0.38 inference(negative_extensionality,[],[f33])).
% 0.24/0.38 thf(f35,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true) | ((((^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)) @ sK2)) = $true)),
% 0.24/0.38 inference(xor_proxy_clausification,[],[f34])).
% 0.24/0.38 thf(f36,plain,(
% 0.24/0.38 ($false = (((^[Y0 : $i]: (grandchild_THFTYPE_IiioI @ Y0 @ lJohn_THFTYPE_i)) @ sK2))) | (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $false)),
% 0.24/0.38 inference(xor_proxy_clausification,[],[f34])).
% 0.24/0.38 thf(f37,plain,(
% 0.24/0.38 ($false = ((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i))) | (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $false)),
% 0.24/0.38 inference(beta-eta_normalization,[],[f36])).
% 0.24/0.38 thf(f38,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true) | (((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)) = $true)),
% 0.24/0.38 inference(beta-eta_normalization,[],[f35])).
% 0.24/0.38 thf(f40,definition,(
% 0.24/0.38 spl3_1 <=> (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $false)),
% 0.24/0.38 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.24/0.38 thf(f42,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $false) | ~spl3_1),
% 0.24/0.38 inference(avatar_component_clause,[],[f40])).
% 0.24/0.38 thf(f44,definition,(
% 0.24/0.38 spl3_2 <=> ($false = ((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)))),
% 0.24/0.38 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.24/0.38 thf(f46,plain,(
% 0.24/0.38 ($false = ((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i))) | ~spl3_2),
% 0.24/0.38 inference(avatar_component_clause,[],[f44])).
% 0.24/0.38 thf(f47,plain,(
% 0.24/0.38 spl3_1 | spl3_2),
% 0.24/0.38 inference(avatar_split_clause,[],[f37,f44,f40])).
% 0.24/0.38 thf(f49,definition,(
% 0.24/0.38 spl3_3 <=> (((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)) = $true)),
% 0.24/0.38 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.24/0.38 thf(f51,plain,(
% 0.24/0.38 (((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)) = $true) | ~spl3_3),
% 0.24/0.38 inference(avatar_component_clause,[],[f49])).
% 0.24/0.38 thf(f53,definition,(
% 0.24/0.38 spl3_4 <=> (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true)),
% 0.24/0.38 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.24/0.38 thf(f55,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true) | ~spl3_4),
% 0.24/0.38 inference(avatar_component_clause,[],[f53])).
% 0.24/0.38 thf(f56,plain,(
% 0.24/0.38 spl3_3 | spl3_4),
% 0.24/0.38 inference(avatar_split_clause,[],[f38,f53,f49])).
% 0.24/0.38 thf(f58,plain,(
% 0.24/0.38 ($false = $true) | (~spl3_2 | ~spl3_3)),
% 0.24/0.38 inference(constrained_superposition,[],[f46,f51])).
% 0.24/0.38 thf(f61,plain,(
% 0.24/0.38 $false | (~spl3_2 | ~spl3_3)),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f58])).
% 0.24/0.38 thf(f62,plain,(
% 0.24/0.38 ~spl3_2 | ~spl3_3),
% 0.24/0.38 inference(avatar_contradiction_clause,[],[f61])).
% 0.24/0.38 thf(f64,plain,(
% 0.24/0.38 ($true != $true) | (((parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ (sK0 @ lJohn_THFTYPE_i @ sK2))) = $true) | ~spl3_3),
% 0.24/0.38 inference(constrained_superposition,[],[f22,f51])).
% 0.24/0.38 thf(f65,plain,(
% 0.24/0.38 (((parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ (sK0 @ lJohn_THFTYPE_i @ sK2))) = $true) | ~spl3_3),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.24/0.38 thf(f66,plain,(
% 0.24/0.38 ($true != $true) | (((parent_THFTYPE_IiioI @ (sK0 @ lJohn_THFTYPE_i @ sK2) @ sK2)) = $true) | ~spl3_3),
% 0.24/0.38 inference(constrained_superposition,[],[f23,f51])).
% 0.24/0.38 thf(f67,plain,(
% 0.24/0.38 (((parent_THFTYPE_IiioI @ (sK0 @ lJohn_THFTYPE_i @ sK2) @ sK2)) = $true) | ~spl3_3),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f66])).
% 0.24/0.38 thf(f77,plain,(
% 0.24/0.38 ( ! [X0 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ (sK0 @ lJohn_THFTYPE_i @ sK2))) != $true) | ($true != $true) | (((grandparent_THFTYPE_IiioI @ X0 @ sK2)) = $true)) ) | ~spl3_3),
% 0.24/0.38 inference(constrained_superposition,[],[f28,f67])).
% 0.24/0.38 thf(f79,plain,(
% 0.24/0.38 ( ! [X0 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ (sK0 @ lJohn_THFTYPE_i @ sK2))) != $true) | (((grandparent_THFTYPE_IiioI @ X0 @ sK2)) = $true)) ) | ~spl3_3),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f77])).
% 0.24/0.38 thf(f80,plain,(
% 0.24/0.38 ($true != $true) | (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true) | ~spl3_3),
% 0.24/0.38 inference(constrained_superposition,[],[f79,f65])).
% 0.24/0.38 thf(f81,plain,(
% 0.24/0.38 (((grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ sK2)) = $true) | ~spl3_3),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f80])).
% 0.24/0.38 thf(f82,plain,(
% 0.24/0.38 ($false = $true) | (~spl3_1 | ~spl3_3)),
% 0.24/0.38 inference(forward_demodulation,[],[f81,f42])).
% 0.24/0.38 thf(f83,plain,(
% 0.24/0.38 $false | (~spl3_1 | ~spl3_3)),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f82])).
% 0.24/0.38 thf(f84,plain,(
% 0.24/0.38 ~spl3_1 | ~spl3_3),
% 0.24/0.38 inference(avatar_contradiction_clause,[],[f83])).
% 0.24/0.38 thf(f88,plain,(
% 0.24/0.38 ($true != $true) | (((parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ (sK1 @ sK2 @ lJohn_THFTYPE_i))) = $true) | ~spl3_4),
% 0.24/0.38 inference(constrained_superposition,[],[f27,f55])).
% 0.24/0.38 thf(f89,plain,(
% 0.24/0.38 ($true != $true) | (((parent_THFTYPE_IiioI @ (sK1 @ sK2 @ lJohn_THFTYPE_i) @ sK2)) = $true) | ~spl3_4),
% 0.24/0.38 inference(constrained_superposition,[],[f26,f55])).
% 0.24/0.38 thf(f90,plain,(
% 0.24/0.38 (((parent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ (sK1 @ sK2 @ lJohn_THFTYPE_i))) = $true) | ~spl3_4),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f88])).
% 0.24/0.38 thf(f91,plain,(
% 0.24/0.38 (((parent_THFTYPE_IiioI @ (sK1 @ sK2 @ lJohn_THFTYPE_i) @ sK2)) = $true) | ~spl3_4),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f89])).
% 0.24/0.38 thf(f97,plain,(
% 0.24/0.38 ( ! [X0 : $i] : ((((grandchild_THFTYPE_IiioI @ sK2 @ X0)) = $true) | (((parent_THFTYPE_IiioI @ X0 @ (sK1 @ sK2 @ lJohn_THFTYPE_i))) != $true) | ($true != $true)) ) | ~spl3_4),
% 0.24/0.38 inference(constrained_superposition,[],[f21,f91])).
% 0.24/0.38 thf(f99,plain,(
% 0.24/0.38 ( ! [X0 : $i] : ((((parent_THFTYPE_IiioI @ X0 @ (sK1 @ sK2 @ lJohn_THFTYPE_i))) != $true) | (((grandchild_THFTYPE_IiioI @ sK2 @ X0)) = $true)) ) | ~spl3_4),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f97])).
% 0.24/0.38 thf(f102,plain,(
% 0.24/0.38 (((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)) = $true) | ($true != $true) | ~spl3_4),
% 0.24/0.38 inference(constrained_superposition,[],[f99,f90])).
% 0.24/0.38 thf(f103,plain,(
% 0.24/0.38 (((grandchild_THFTYPE_IiioI @ sK2 @ lJohn_THFTYPE_i)) = $true) | ~spl3_4),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f102])).
% 0.24/0.38 thf(f104,plain,(
% 0.24/0.38 ($false = $true) | (~spl3_2 | ~spl3_4)),
% 0.24/0.38 inference(forward_demodulation,[],[f103,f46])).
% 0.24/0.38 thf(f105,plain,(
% 0.24/0.38 $false | (~spl3_2 | ~spl3_4)),
% 0.24/0.38 inference(trivial_inequality_removal,[],[f104])).
% 0.24/0.38 thf(f106,plain,(
% 0.24/0.38 ~spl3_2 | ~spl3_4),
% 0.24/0.38 inference(avatar_contradiction_clause,[],[f105])).
% 0.24/0.38 thf(f107,plain,(
% 0.24/0.38 spl3_3 | ~spl3_4),
% 0.24/0.38 inference(avatar_split_clause,[],[f103,f53,f49])).
% 0.24/0.38 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f47])).
% 0.24/0.38 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f56])).
% 0.24/0.38 cnf(s4, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f62])).
% 0.24/0.38 cnf(s5, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f84])).
% 0.24/0.38 cnf(s6, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f106])).
% 0.24/0.38 cnf(s7, plain, spl3_3 | ~spl3_4, inference(sat_conversion,[],[f107])).
% 0.24/0.38 cnf(s8, plain, ~spl3_2, inference(rat,[],[s2,s4,s6])).
% 0.24/0.38 cnf(s9, plain, spl3_1, inference(rat,[],[s1,s8])).
% 0.24/0.38 cnf(s10, plain, ~spl3_3, inference(rat,[],[s5,s9])).
% 0.24/0.38 cnf(s11, plain, ~spl3_4, inference(rat,[],[s7,s10])).
% 0.24/0.38 cnf(s12, plain, $false, inference(rat,[],[s2,s11,s10])).
% 0.24/0.38 thf(f108,plain,(
% 0.24/0.38 $false),
% 0.24/0.38 inference(avatar_sat_refutation,[],[s12])).
% 0.24/0.38 % SZS output end Proof for theBenchmark
% 0.24/0.38 % (1098713)------------------------------
% 0.24/0.38 % (1098713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.38 % (1098713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.38 % (1098713)CaDiCaL version: 2.1.3
% 0.24/0.38 % (1098713)Termination reason: Refutation
% 0.24/0.38 % (1098713)Time elapsed: 0.011 s
% 0.24/0.38 % (1098713)Peak memory usage: 13 MB
% 0.24/0.38 % (1098713)Instructions burned: 9 (million)
% 0.24/0.38 % (1098707)Success in time 0.048 s
% 0.24/0.38 % Vampire exiting
%------------------------------------------------------------------------------