%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n014.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 : Mon Sep 7 11:13:01 AM UTC 2026
% Result : Theorem 12.85s 4.34s
% Output : CNFRefutation 12.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL947_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 00:01:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 12.85/4.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.85/4.35
% 12.85/4.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.85/4.36 %$ subset > qmltpeq > member > union > #nlpp > #skF_33 > #skF_26 > #skF_9 > #skF_16 > #skF_22 > #skF_30 > #skF_1 > #skF_4 > #skF_13 > #skF_32 > #skF_7 > #skF_38 > #skF_11 > #skF_8 > #skF_18 > #skF_5 > #skF_2 > #skF_28 > #skF_6 > #skF_17 > #skF_20 > #skF_29 > #skF_36 > #skF_37 > #skF_3 > #skF_27 > #skF_31 > #skF_25 > #skF_15 > #skF_34 > #skF_19 > #skF_12 > #skF_14 > #skF_39 > #skF_21 > #skF_35 > #skF_10 > #skF_23 > #skF_24
% 12.85/4.36
% 12.85/4.36 %Foreground sorts:
% 12.85/4.36 tff($ki_world, type, $ki_world: $tType ).
% 12.85/4.36
% 12.85/4.36 %Background operators:
% 12.85/4.36
% 12.85/4.36
% 12.85/4.36 %Foreground operators:
% 12.85/4.36 tff('#skF_33', type, '#skF_33': ($i * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff(subset, type, subset: ($ki_world * $i * $i) > $o).
% 12.85/4.36 tff('#skF_26', type, '#skF_26': ($ki_world * $ki_world * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_9', type, '#skF_9': ($i * $i * $ki_world * $ki_world * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_16', type, '#skF_16': ($ki_world * $ki_world * $i * $ki_world * $i * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_22', type, '#skF_22': ($ki_world * $ki_world * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_30', type, '#skF_30': ($ki_world * $i * $i * $ki_world * $ki_world * $ki_world * $i * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_1', type, '#skF_1': $ki_world > $i).
% 12.85/4.36 tff('#skF_4', type, '#skF_4': ($ki_world * $ki_world * $ki_world * $i * $i * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_13', type, '#skF_13': ($i * $i * $ki_world * $i * $ki_world * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_32', type, '#skF_32': ($i * $ki_world * $ki_world * $ki_world * $i) > $i).
% 12.85/4.36 tff(member, type, member: ($ki_world * $i * $i) > $o).
% 12.85/4.36 tff('#skF_7', type, '#skF_7': ($ki_world * $ki_world * $ki_world * $ki_world * $i * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_38', type, '#skF_38': $i).
% 12.85/4.36 tff(union, type, union: ($i * $i) > $i).
% 12.85/4.36 tff('#skF_11', type, '#skF_11': ($i * $i * $ki_world * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_8', type, '#skF_8': ($ki_world * $ki_world * $ki_world * $ki_world * $i * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_18', type, '#skF_18': ($ki_world * $ki_world * $i * $i * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_5', type, '#skF_5': ($ki_world * $ki_world * $i * $ki_world * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_2', type, '#skF_2': ($i * $ki_world * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_28', type, '#skF_28': ($i * $ki_world * $ki_world * $i * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_6', type, '#skF_6': ($ki_world * $ki_world * $i * $i * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_17', type, '#skF_17': ($ki_world * $ki_world * $i * $i * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_20', type, '#skF_20': ($ki_world * $i * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_29', type, '#skF_29': ($i * $i * $ki_world * $ki_world * $ki_world * $ki_world * $i * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_36', type, '#skF_36': ($i * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_37', type, '#skF_37': $ki_world).
% 12.85/4.36 tff('#skF_3', type, '#skF_3': ($ki_world * $ki_world * $ki_world * $i * $i * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff(qmltpeq, type, qmltpeq: ($ki_world * $i * $i) > $o).
% 12.85/4.36 tff('#skF_27', type, '#skF_27': ($ki_world * $ki_world * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_31', type, '#skF_31': ($i * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_25', type, '#skF_25': ($ki_world * $ki_world * $ki_world * $i * $i) > $i).
% 12.85/4.36 tff('#skF_15', type, '#skF_15': ($ki_world * $i * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_34', type, '#skF_34': ($i * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_19', type, '#skF_19': ($ki_world * $i * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_12', type, '#skF_12': ($i * $i * $ki_world * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_14', type, '#skF_14': ($i * $i * $ki_world * $i * $ki_world * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_39', type, '#skF_39': $ki_world).
% 12.85/4.36 tff('#skF_21', type, '#skF_21': ($ki_world * $i * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_35', type, '#skF_35': ($i * $ki_world * $ki_world * $ki_world * $i) > $ki_world).
% 12.85/4.36 tff('#skF_10', type, '#skF_10': ($i * $i * $ki_world * $ki_world * $i * $ki_world * $ki_world) > $ki_world).
% 12.85/4.36 tff('#skF_23', type, '#skF_23': ($ki_world * $ki_world * $ki_world * $ki_world * $i * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36 tff('#skF_24', type, '#skF_24': ($ki_world * $ki_world * $ki_world * $i * $i) > $ki_world).
% 12.85/4.36
% 12.85/4.38 tff(f_625, negated_conjecture, ~(![W:$ki_world]: ($ki_accessible($ki_local_world, W) => (![B]: ($ki_exists_in_world_$i(W, B) => (![W0:$ki_world]: ($ki_accessible(W, W0) => qmltpeq(W0, union(B, B), B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', verify)).
% 12.85/4.38 tff(f_30, axiom, (![W:$ki_world]: $ki_accessible(W, W)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mrel_reflexive)).
% 12.85/4.38 tff(f_332, axiom, (![W:$ki_world]: ($ki_accessible($ki_local_world, W) => (![B]: ($ki_exists_in_world_$i(W, B) => (![W0:$ki_world]: ($ki_accessible(W, W0) => (![C]: ($ki_exists_in_world_$i(W0, C) => (![W1:$ki_world]: ($ki_accessible(W0, W1) => ((![W2:$ki_world]: ($ki_accessible(W1, W2) => subset(W2, B, C))) => (![W2:$ki_world]: ($ki_accessible(W1, W2) => qmltpeq(W2, union(B, C), C)))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset_union)).
% 12.85/4.38 tff(f_523, axiom, (![W:$ki_world]: ($ki_accessible($ki_local_world, W) => (![B]: ($ki_exists_in_world_$i(W, B) => (![W0:$ki_world]: ($ki_accessible(W, W0) => subset(W0, B, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', reflexivity_of_subset)).
% 12.85/4.38 tff(c_172, plain, ($ki_accessible('#skF_37', '#skF_39')), inference(cnfTransformation, [status(thm)], [f_625])).
% 12.85/4.38 tff(c_176, plain, ($ki_accessible($ki_local_world, '#skF_37')), inference(cnfTransformation, [status(thm)], [f_625])).
% 12.85/4.38 tff(c_2, plain, (![W_1:$ki_world]: ($ki_accessible(W_1, W_1))), inference(cnfTransformation, [status(thm)], [f_30])).
% 12.85/4.38 tff(c_174, plain, ($ki_exists_in_world_$i('#skF_37', '#skF_38')), inference(cnfTransformation, [status(thm)], [f_625])).
% 12.85/4.38 tff(c_1762, plain, (![W_9484:$ki_world, W1_9479:$ki_world, C_9481, W2_9480:$ki_world, W0_9483:$ki_world, B_9482]: ($ki_accessible(W1_9479, '#skF_15'(W1_9479, C_9481, B_9482, W0_9483, W_9484)) | qmltpeq(W2_9480, union(B_9482, C_9481), C_9481) | ~$ki_accessible(W1_9479, W2_9480) | ~$ki_accessible(W0_9483, W1_9479) | ~$ki_exists_in_world_$i(W0_9483, C_9481) | ~$ki_accessible(W_9484, W0_9483) | ~$ki_exists_in_world_$i(W_9484, B_9482) | ~$ki_accessible($ki_local_world, W_9484))), inference(cnfTransformation, [status(thm)], [f_332])).
% 12.85/4.38 tff(c_1895, plain, (![C_9485, B_9486, W0_9487:$ki_world, W_9488:$ki_world]: ($ki_accessible('#skF_37', '#skF_15'('#skF_37', C_9485, B_9486, W0_9487, W_9488)) | qmltpeq('#skF_39', union(B_9486, C_9485), C_9485) | ~$ki_accessible(W0_9487, '#skF_37') | ~$ki_exists_in_world_$i(W0_9487, C_9485) | ~$ki_accessible(W_9488, W0_9487) | ~$ki_exists_in_world_$i(W_9488, B_9486) | ~$ki_accessible($ki_local_world, W_9488))), inference(resolution, [status(thm)], [c_172, c_1762])).
% 12.85/4.38 tff(c_170, plain, (~qmltpeq('#skF_39', union('#skF_38', '#skF_38'), '#skF_38')), inference(cnfTransformation, [status(thm)], [f_625])).
% 12.85/4.38 tff(c_1939, plain, (![W0_9489:$ki_world, W_9490:$ki_world]: ($ki_accessible('#skF_37', '#skF_15'('#skF_37', '#skF_38', '#skF_38', W0_9489, W_9490)) | ~$ki_accessible(W0_9489, '#skF_37') | ~$ki_exists_in_world_$i(W0_9489, '#skF_38') | ~$ki_accessible(W_9490, W0_9489) | ~$ki_exists_in_world_$i(W_9490, '#skF_38') | ~$ki_accessible($ki_local_world, W_9490))), inference(resolution, [status(thm)], [c_1895, c_170])).
% 12.85/4.38 tff(c_116, plain, (![W0_6317:$ki_world, B_6315, W_6311:$ki_world]: (subset(W0_6317, B_6315, B_6315) | ~$ki_accessible(W_6311, W0_6317) | ~$ki_exists_in_world_$i(W_6311, B_6315) | ~$ki_accessible($ki_local_world, W_6311))), inference(cnfTransformation, [status(thm)], [f_523])).
% 12.85/4.38 tff(c_1957, plain, (![W0_9489:$ki_world, W_9490:$ki_world, B_6315]: (subset('#skF_15'('#skF_37', '#skF_38', '#skF_38', W0_9489, W_9490), B_6315, B_6315) | ~$ki_exists_in_world_$i('#skF_37', B_6315) | ~$ki_accessible($ki_local_world, '#skF_37') | ~$ki_accessible(W0_9489, '#skF_37') | ~$ki_exists_in_world_$i(W0_9489, '#skF_38') | ~$ki_accessible(W_9490, W0_9489) | ~$ki_exists_in_world_$i(W_9490, '#skF_38') | ~$ki_accessible($ki_local_world, W_9490))), inference(resolution, [status(thm)], [c_1939, c_116])).
% 12.85/4.38 tff(c_1974, plain, (![W0_9489:$ki_world, W_9490:$ki_world, B_6315]: (subset('#skF_15'('#skF_37', '#skF_38', '#skF_38', W0_9489, W_9490), B_6315, B_6315) | ~$ki_exists_in_world_$i('#skF_37', B_6315) | ~$ki_accessible(W0_9489, '#skF_37') | ~$ki_exists_in_world_$i(W0_9489, '#skF_38') | ~$ki_accessible(W_9490, W0_9489) | ~$ki_exists_in_world_$i(W_9490, '#skF_38') | ~$ki_accessible($ki_local_world, W_9490))), inference(demodulation, [status(thm), theory('equality')], [c_176, c_1957])).
% 12.85/4.38 tff(c_2170, plain, (![W1_9514:$ki_world, W2_9515:$ki_world, B_9517, C_9516, W_9519:$ki_world, W0_9518:$ki_world]: (~subset('#skF_15'(W1_9514, C_9516, B_9517, W0_9518, W_9519), B_9517, C_9516) | qmltpeq(W2_9515, union(B_9517, C_9516), C_9516) | ~$ki_accessible(W1_9514, W2_9515) | ~$ki_accessible(W0_9518, W1_9514) | ~$ki_exists_in_world_$i(W0_9518, C_9516) | ~$ki_accessible(W_9519, W0_9518) | ~$ki_exists_in_world_$i(W_9519, B_9517) | ~$ki_accessible($ki_local_world, W_9519))), inference(cnfTransformation, [status(thm)], [f_332])).
% 12.85/4.38 tff(c_2173, plain, (![W2_9515:$ki_world, W0_9489:$ki_world, W_9490:$ki_world]: (qmltpeq(W2_9515, union('#skF_38', '#skF_38'), '#skF_38') | ~$ki_accessible('#skF_37', W2_9515) | ~$ki_exists_in_world_$i('#skF_37', '#skF_38') | ~$ki_accessible(W0_9489, '#skF_37') | ~$ki_exists_in_world_$i(W0_9489, '#skF_38') | ~$ki_accessible(W_9490, W0_9489) | ~$ki_exists_in_world_$i(W_9490, '#skF_38') | ~$ki_accessible($ki_local_world, W_9490))), inference(resolution, [status(thm)], [c_1974, c_2170])).
% 12.85/4.38 tff(c_2179, plain, (![W2_9515:$ki_world, W0_9489:$ki_world, W_9490:$ki_world]: (qmltpeq(W2_9515, union('#skF_38', '#skF_38'), '#skF_38') | ~$ki_accessible('#skF_37', W2_9515) | ~$ki_accessible(W0_9489, '#skF_37') | ~$ki_exists_in_world_$i(W0_9489, '#skF_38') | ~$ki_accessible(W_9490, W0_9489) | ~$ki_exists_in_world_$i(W_9490, '#skF_38') | ~$ki_accessible($ki_local_world, W_9490))), inference(demodulation, [status(thm), theory('equality')], [c_174, c_2173])).
% 12.85/4.38 tff(c_2182, plain, (![W0_9520:$ki_world, W_9521:$ki_world]: (~$ki_accessible(W0_9520, '#skF_37') | ~$ki_exists_in_world_$i(W0_9520, '#skF_38') | ~$ki_accessible(W_9521, W0_9520) | ~$ki_exists_in_world_$i(W_9521, '#skF_38') | ~$ki_accessible($ki_local_world, W_9521))), inference(splitLeft, [status(thm)], [c_2179])).
% 12.85/4.38 tff(c_2184, plain, (![W_9521:$ki_world]: (~$ki_accessible('#skF_37', '#skF_37') | ~$ki_accessible(W_9521, '#skF_37') | ~$ki_exists_in_world_$i(W_9521, '#skF_38') | ~$ki_accessible($ki_local_world, W_9521))), inference(resolution, [status(thm)], [c_174, c_2182])).
% 12.85/4.38 tff(c_2188, plain, (![W_9522:$ki_world]: (~$ki_accessible(W_9522, '#skF_37') | ~$ki_exists_in_world_$i(W_9522, '#skF_38') | ~$ki_accessible($ki_local_world, W_9522))), inference(demodulation, [status(thm), theory('equality')], [c_2, c_2184])).
% 12.85/4.38 tff(c_2191, plain, (~$ki_accessible('#skF_37', '#skF_37') | ~$ki_accessible($ki_local_world, '#skF_37')), inference(resolution, [status(thm)], [c_174, c_2188])).
% 12.85/4.38 tff(c_2195, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_176, c_2, c_2191])).
% 12.85/4.38 tff(c_2241, plain, (![W2_9527:$ki_world]: (qmltpeq(W2_9527, union('#skF_38', '#skF_38'), '#skF_38') | ~$ki_accessible('#skF_37', W2_9527))), inference(splitRight, [status(thm)], [c_2179])).
% 12.85/4.38 tff(c_2253, plain, (~$ki_accessible('#skF_37', '#skF_39')), inference(resolution, [status(thm)], [c_2241, c_170])).
% 12.85/4.38 tff(c_2260, plain, $false, inference(demodulation, [status(thm), theory('equality')], [c_172, c_2253])).
% 12.85/4.38 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------